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k a March Highlights and 2025 AoPS Online Class Information
jlacosta   0
Mar 2, 2025
March is the month for State MATHCOUNTS competitions! Kudos to everyone who participated in their local chapter competitions and best of luck to all going to State! Join us on March 11th for a Math Jam devoted to our favorite Chapter competition problems! Are you interested in training for MATHCOUNTS? Be sure to check out our AMC 8/MATHCOUNTS Basics and Advanced courses.

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Do you have plans this summer? There are so many options to fit your schedule and goals whether attending a summer camp or taking online classes, it can be a great break from the routine of the school year. Check out our summer courses at AoPS Online, or if you want a math or language arts class that doesn’t have homework, but is an enriching summer experience, our AoPS Virtual Campus summer camps may be just the ticket! We are expanding our locations for our AoPS Academies across the country with 15 locations so far and new campuses opening in Saratoga CA, Johns Creek GA, and the Upper West Side NY. Check out this page for summer camp information.

Be sure to mark your calendars for the following events:
[list][*]March 5th (Wednesday), 4:30pm PT/7:30pm ET, HCSSiM Math Jam 2025. Amber Verser, Assistant Director of the Hampshire College Summer Studies in Mathematics, will host an information session about HCSSiM, a summer program for high school students.
[*]March 6th (Thursday), 4:00pm PT/7:00pm ET, Free Webinar on Math Competitions from elementary through high school. Join us for an enlightening session that demystifies the world of math competitions and helps you make informed decisions about your contest journey.
[*]March 11th (Tuesday), 4:30pm PT/7:30pm ET, 2025 MATHCOUNTS Chapter Discussion MATH JAM. AoPS instructors will discuss some of their favorite problems from the MATHCOUNTS Chapter Competition. All are welcome!
[*]March 13th (Thursday), 4:00pm PT/7:00pm ET, Free Webinar about Summer Camps at the Virtual Campus. Transform your summer into an unforgettable learning adventure! From elementary through high school, we offer dynamic summer camps featuring topics in mathematics, language arts, and competition preparation - all designed to fit your schedule and ignite your passion for learning.[/list]
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0 replies
jlacosta
Mar 2, 2025
0 replies
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k i Adding contests to the Contest Collections
dcouchman   1
N Apr 5, 2023 by v_Enhance
Want to help AoPS remain a valuable Olympiad resource? Help us add contests to AoPS's Contest Collections.

Find instructions and a list of contests to add here: https://artofproblemsolving.com/community/c40244h1064480_contests_to_add
1 reply
dcouchman
Sep 9, 2019
v_Enhance
Apr 5, 2023
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k i Zero tolerance
ZetaX   49
N May 4, 2019 by NoDealsHere
Source: Use your common sense! (enough is enough)
Some users don't want to learn, some other simply ignore advises.
But please follow the following guideline:


To make it short: ALWAYS USE YOUR COMMON SENSE IF POSTING!
If you don't have common sense, don't post.


More specifically:

For new threads:


a) Good, meaningful title:
The title has to say what the problem is about in best way possible.
If that title occured already, it's definitely bad. And contest names aren't good either.
That's in fact a requirement for being able to search old problems.

Examples:
Bad titles:
- "Hard"/"Medium"/"Easy" (if you find it so cool how hard/easy it is, tell it in the post and use a title that tells us the problem)
- "Number Theory" (hey guy, guess why this forum's named that way¿ and is it the only such problem on earth¿)
- "Fibonacci" (there are millions of Fibonacci problems out there, all posted and named the same...)
- "Chinese TST 2003" (does this say anything about the problem¿)
Good titles:
- "On divisors of a³+2b³+4c³-6abc"
- "Number of solutions to x²+y²=6z²"
- "Fibonacci numbers are never squares"


b) Use search function:
Before posting a "new" problem spend at least two, better five, minutes to look if this problem was posted before. If it was, don't repost it. If you have anything important to say on topic, post it in one of the older threads.
If the thread is locked cause of this, use search function.

Update (by Amir Hossein). The best way to search for two keywords in AoPS is to input
[code]+"first keyword" +"second keyword"[/code]
so that any post containing both strings "first word" and "second form".


c) Good problem statement:
Some recent really bad post was:
[quote]$lim_{n\to 1}^{+\infty}\frac{1}{n}-lnn$[/quote]
It contains no question and no answer.
If you do this, too, you are on the best way to get your thread deleted. Write everything clearly, define where your variables come from (and define the "natural" numbers if used). Additionally read your post at least twice before submitting. After you sent it, read it again and use the Edit-Button if necessary to correct errors.


For answers to already existing threads:


d) Of any interest and with content:
Don't post things that are more trivial than completely obvious. For example, if the question is to solve $x^{3}+y^{3}=z^{3}$, do not answer with "$x=y=z=0$ is a solution" only. Either you post any kind of proof or at least something unexpected (like "$x=1337, y=481, z=42$ is the smallest solution). Someone that does not see that $x=y=z=0$ is a solution of the above without your post is completely wrong here, this is an IMO-level forum.
Similar, posting "I have solved this problem" but not posting anything else is not welcome; it even looks that you just want to show off what a genius you are.

e) Well written and checked answers:
Like c) for new threads, check your solutions at least twice for mistakes. And after sending, read it again and use the Edit-Button if necessary to correct errors.



To repeat it: ALWAYS USE YOUR COMMON SENSE IF POSTING!


Everything definitely out of range of common sense will be locked or deleted (exept for new users having less than about 42 posts, they are newbies and need/get some time to learn).

The above rules will be applied from next monday (5. march of 2007).
Feel free to discuss on this here.
49 replies
ZetaX
Feb 27, 2007
NoDealsHere
May 4, 2019
J
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Geometry solutions needed of pathfinder senior
SHIVAM_OP-IMO2025   1
N 43 minutes ago by S.Ragnork1729
Someone plzz share pathfinder senior by vikas tiwari solutions..
1 reply
SHIVAM_OP-IMO2025
an hour ago
S.Ragnork1729
43 minutes ago
J
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funny title placeholder
pikapika007   46
N an hour ago by aliz
Source: USAJMO 2025/6
Let $S$ be a set of integers with the following properties:
[list]
[*] $\{ 1, 2, \dots, 2025 \} \subseteq S$.
[*] If $a, b \in S$ and $\gcd(a, b) = 1$, then $ab \in S$.
[*] If for some $s \in S$, $s + 1$ is composite, then all positive divisors of $s + 1$ are in $S$.
[/list]
Prove that $S$ contains all positive integers.
46 replies
pikapika007
Yesterday at 12:10 PM
aliz
an hour ago
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new playlist in Olympiad Geometry Channel
Plane_geometry_youtuber   3
N an hour ago by SHIVAM_OP-IMO2025
Hi,

I create a new playlist called "Problems from Audience". I will put my solution of the problems from audience into this playlist. Welcome to send me your problems and doubts.

https://www.youtube.com/@OlympiadGeometry-2024

my email: planery.geometry@gmail.com
3 replies
Plane_geometry_youtuber
Jan 28, 2025
SHIVAM_OP-IMO2025
an hour ago
J
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Prove that $\angle FAC = \angle EDB$
micliva   26
N an hour ago by cappucher
Source: All-Russian Olympiad 1996, Grade 10, First Day, Problem 1
Points $E$ and $F$ are given on side $BC$ of convex quadrilateral $ABCD$ (with $E$ closer than $F$ to $B$). It is known that $\angle BAE = \angle CDF$ and $\angle EAF = \angle FDE$. Prove that $\angle FAC = \angle EDB$.

M. Smurov
26 replies
micliva
Apr 18, 2013
cappucher
an hour ago
J
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Scary Binomial Coefficient Sum
EpicBird08   31
N an hour ago by john0512
Source: USAMO 2025/5
Determine, with proof, all positive integers $k$ such that $$\frac{1}{n+1} \sum_{i=0}^n \binom{n}{i}^k$$is an integer for every positive integer $n.$
31 replies
EpicBird08
Yesterday at 11:59 AM
john0512
an hour ago
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Find all m,n such that...
srnjbr   0
2 hours ago
Suppose that m,n are in natural numbers. find all m,n that (m^n-n)^m=n!+m
0 replies
srnjbr
2 hours ago
0 replies
J
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sequence and number theory
srnjbr   0
2 hours ago
Let a1 be a member of the integers and an+1=an^2-an-1. Show that (an+1,2n+1)=1
0 replies
srnjbr
2 hours ago
0 replies
J
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2022 Junior Balkan MO, Problem 1
sarjinius   25
N 2 hours ago by anudeep
Source: 2022 JBMO Problem 1
Find all pairs of positive integers $(a, b)$ such that $$11ab \le a^3 - b^3 \le 12ab.$$
25 replies
sarjinius
Jun 30, 2022
anudeep
2 hours ago
J
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Mathroots
Ruegerbyrd   0
2 hours ago
Has anyone gotten acceptances from MIT's Mathroots yet? Did they ever say they wouldn't send letters to anyone unless accepted?
0 replies
Ruegerbyrd
2 hours ago
0 replies
J
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Nice function question
srnjbr   0
2 hours ago
Find all functions f:R+--R+ such that for all a,b>0, f(af(b)+a)(f(bf(a))+a)=1
0 replies
srnjbr
2 hours ago
0 replies
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[TEST RELEASED] Mock Geometry Test for College Competitions
Bluesoul   16
N 2 hours ago by lord_of_the_rook
Hi AOPSers,

I have finished writing a mock geometry test for fun and practice for the real college competitions like HMMT/PUMaC/CMIMC... There would be 10 questions and you should finish the test in 60 minutes, the test would be close to the actual test (hopefully). You could sign up under this thread, PM me your answers!. The submission would close on March 31st at 11:59PM PST.

I would create a private discussion forum so everyone could discuss after finishing the test. This is the first mock I've written, please sign up and enjoy geometry!!

~Bluesoul

Leaderboard
16 replies
Bluesoul
Feb 24, 2025
lord_of_the_rook
2 hours ago
J
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Find min
hunghd8   6
N 2 hours ago by imnotgoodatmathsorry
Let $a,b,c$ be nonnegative real numbers such that $ a+b+c\geq 2+abc $. Find min
$$P=a^2+b^2+c^2.$$
6 replies
hunghd8
Yesterday at 12:10 PM
imnotgoodatmathsorry
2 hours ago
J
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Interesting inequality
sqing   1
N 2 hours ago by ionbursuc
Source: Own
Let $ a,b> 0$ and $ a+b=1 . $ Prove that
$$ \frac{1}{a}+\frac{1}{b}\geq \frac{2k}{1+k^2 a^2b^2}$$Where $ 5\leq k\in N^+.$
1 reply
sqing
3 hours ago
ionbursuc
2 hours ago
J
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Inequality
srnjbr   1
N 3 hours ago by sqing
a^2+b^2+c^2+x^2+y^2=1. Find the maximum value of the expression (ax+by)^2+(bx+cy)^2
1 reply
srnjbr
Yesterday at 4:32 PM
sqing
3 hours ago
J
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Mock AMC G
paladin8   31
N Feb 11, 2008 by Ignite168
Anyway, here's yet another Mock AMC. I tried really hard, so if it's bad, don't say anything or I'll feel really bad and go cry. In any case, rules are the same as usual; the test has been checked over, so any ambiguities should be resolved. Otherwise, post it in this thread (general questions) or PM me (specific questions, related to answers). Difficulty should be fairly consistent with AMC problems, not that I would know, but that's ok. Enjoy!

The Test

Oh, and regarding submitting answers, I guess I'll do all that scoring, ranking, etc. just PM me your answers. You'll have a week or so, so let's say due by next Wednesday 1/17.
31 replies
paladin8
Jan 11, 2007
Ignite168
Feb 11, 2008
J
Mock AMC G
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Reveal topic tags
geometry
email
AMC
L
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paladin8
3237 posts
paladin8
#1 h  Jan 11, 2007, 6:28 AM • 2 Y
Y by Adventure10, Mango247
Anyway, here's yet another Mock AMC. I tried really hard, so if it's bad, don't say anything or I'll feel really bad and go cry. In any case, rules are the same as usual; the test has been checked over, so any ambiguities should be resolved. Otherwise, post it in this thread (general questions) or PM me (specific questions, related to answers). Difficulty should be fairly consistent with AMC problems, not that I would know, but that's ok. Enjoy!

The Test

Oh, and regarding submitting answers, I guess I'll do all that scoring, ranking, etc. just PM me your answers. You'll have a week or so, so let's say due by next Wednesday 1/17.
Attachments:
mockAMC.pdf (111kb)
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mysmartmouth
2104 posts
mysmartmouth
#2 h  Jan 11, 2007, 5:40 PM • 4 Y
Y by Adventure10, Mango247, Mango247, Mango247
OK, I won't post my test until yours ends. The letters should have been switched...but whatever. I'm gonna take this right now!

#6 - Is this missing something?
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paladin8
3237 posts
paladin8
#3 h  Jan 11, 2007, 6:23 PM • 2 Y
Y by Adventure10, Mango247
mysmartmouth wrote:
OK, I won't post my test until yours ends. The letters should have been switched...but whatever. I'm gonna take this right now!

#6 - Is this missing something?

As far as I know, it's solvable. It might seem a little ambiguous, but just don't think too hard about it.
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Phelpedo
2444 posts
Phelpedo
#4 h  Jan 11, 2007, 7:30 PM • 1 Y
Y by Adventure10
I suppose the lack of "never" as an answer choice makes it answerable.
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mysmartmouth
2104 posts
mysmartmouth
#5 h  Jan 11, 2007, 9:43 PM • 2 Y
Y by Adventure10, Mango247
I just wanted to add that I HATE geometry, but I really liked every geometry problem you had on the test. Nice job with those. But why must there be trig... :moose:
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paladin8
3237 posts
paladin8
#6 h  Jan 11, 2007, 9:46 PM • 2 Y
Y by Adventure10, Mango247
mysmartmouth wrote:
I just wanted to add that I HATE geometry, but I really liked every geometry problem you had on the test.

Perhaps we have a common interest here...
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purple plume
40 posts
purple plume
#7 h  Jan 11, 2007, 10:02 PM • 1 Y
Y by Adventure10
paladin8 wrote:
mysmartmouth wrote:
I just wanted to add that I HATE geometry, but I really liked every geometry problem you had on the test.

Perhaps we have a common interest here...
That means the writer is mighty talented.
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Altheman
6194 posts
Altheman
#8 h  Jan 11, 2007, 10:15 PM • 2 Y
Y by Adventure10, Mango247
nicely done...the problems feel like those of an actual amc [probably 12]...20,21,24 are nice problems
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mysmartmouth
2104 posts
mysmartmouth
#9 h  Jan 11, 2007, 10:26 PM • 1 Y
Y by Adventure10
I liked 21 and 24 a lot too. 24 is probably too easy for a 24, but I'm not complaining :wink:\

EDIT: wtf purple plume...or should i say now a ranger... change your avatar.

EDIT: Haha we'll see = Sean did something stupid and thinks he solved the problem.
This post has been edited 2 times. Last edited by mysmartmouth, Jan 11, 2007, 10:35 PM
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paladin8
3237 posts
paladin8
#10 h  Jan 11, 2007, 10:31 PM • 2 Y
Y by Adventure10, Mango247
mysmartmouth wrote:
I liked 21 and 24 a lot too. 24 is probably too easy for a 24, but I'm not complaining :wink:

Haha, we'll see.
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aahmadi
223 posts
aahmadi
#11 h  Jan 12, 2007, 2:49 AM • 2 Y
Y by Adventure10, Mango247
i look forward to ur test paladin
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arjunlandes
133 posts
arjunlandes
#12 h  Jan 13, 2007, 9:07 PM • 2 Y
Y by Adventure10, Mango247
Hmm...can you check 17? Maybe I'm being stupid, but I don't see the right answer there.
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paladin8
3237 posts
paladin8
#13 h  Jan 14, 2007, 2:44 AM • 2 Y
Y by Adventure10, Mango247
arjunlandes wrote:
Hmm...can you check 17? Maybe I'm being stupid, but I don't see the right answer there.

I'm pretty sure it's there. If you want, I can PM you the solution (unless you are taking the test and wish to submit answers, of course).
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arjunlandes
133 posts
arjunlandes
#14 h  Jan 14, 2007, 5:47 AM • 2 Y
Y by Adventure10, Mango247
I'm taking the test, so I'll look at it again. Just to be sure, loglog|x| means log of the log of |x|, right?
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paladin8
3237 posts
paladin8
#15 h  Jan 14, 2007, 6:10 AM • 2 Y
Y by Adventure10, Mango247
arjunlandes wrote:
I'm taking the test, so I'll look at it again. Just to be sure, loglog|x| means log of the log of |x|, right?

Yup.

The message contains only quote and code tags. Please add some text of your own.
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xxreddevilzxx
1312 posts
xxreddevilzxx
#16 h  Jan 14, 2007, 7:35 AM • 2 Y
Y by Adventure10, Mango247
I see the answer to #17
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mysmartmouth
2104 posts
mysmartmouth
#17 h  Jan 14, 2007, 8:34 PM • 2 Y
Y by Adventure10, Mango247
Haha, 25 was a beast. Nice problem. Did you make that up? If not, I wanna know the source (after the competition ends).
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King Paul
53 posts
King Paul
#18 h  Jan 14, 2007, 8:36 PM • 2 Y
Y by Adventure10, Mango247
I'm sorry but I don't understand number 6. I don't see what it means.


Yes. the test is very beastly.
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eryaman
1130 posts
eryaman
#19 h  Jan 14, 2007, 8:37 PM • 2 Y
Y by Adventure10, Mango247
Paladin8, I added this Mock AMC to the wiki.
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mysmartmouth
2104 posts
mysmartmouth
#20 h  Jan 14, 2007, 8:45 PM • 2 Y
Y by Adventure10, Mango247
Number 6 might be worded incorrectly, I'm not sure. But just use common sense and you'll see what the writer meant.
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paladin8
3237 posts
paladin8
#21 h  Jan 14, 2007, 9:58 PM • 2 Y
Y by Adventure10, Mango247
mysmartmouth wrote:
Haha, 25 was a beast. Nice problem. Did you make that up? If not, I wanna know the source (after the competition ends).

I did make it up. All the problems are original :).
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bpms
3970 posts
bpms
#22 h  Jan 15, 2007, 1:24 AM • 1 Y
Y by Adventure10
When is this due?
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paladin8
3237 posts
paladin8
#23 h  Jan 15, 2007, 1:49 AM • 1 Y
Y by Adventure10
bpms wrote:
When is this due?

Wednesday, 1/17. At night, I guess. Whatever.
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paladin8
3237 posts
paladin8
#24 h  Jan 15, 2007, 2:50 AM • 2 Y
Y by Adventure10, Mango247
arjunlandes wrote:
Hmm...can you check 17? Maybe I'm being stupid, but I don't see the right answer there.

I apologize to everyone who has taken the test. arjunlandes is corret; the right answer choice was not there for question 17, the point will be given to everyone. The correct answer should be $4 \cdot (10^{\frac{1}{10}}-1)^{2}$.

EDIT: I won't be sending the new scores (you can calculate that), but they will affect the rankings/stats at the end. Also, please use the LINK from now on; it has the newest version (reworded question 6 and changed the answer choices for question 17).
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jyang
1 post
jyang
#25 h  Jan 15, 2007, 4:10 AM • 2 Y
Y by Adventure10, Mango247
Thanks for the test. The author must be really brilliant... :)
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CornOnTheCobbe
3 posts
CornOnTheCobbe
#26 h  Jan 15, 2007, 7:34 PM • 2 Y
Y by Adventure10, Mango247
Please sign me up to take this test also.
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paladin8
3237 posts
paladin8
#27 h  Jan 18, 2007, 12:29 AM • 2 Y
Y by Adventure10, Mango247
Today's the last day to submit answers. I should have results/statistics up by tomorrow.
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Ubemaya
1560 posts
Ubemaya
#28 h  Jan 19, 2007, 1:41 AM • 2 Y
Y by Adventure10, Mango247
Can I turn it in today?

I didn't hear about it until today...

and if I can't, can I just submit it to see what score I got?
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paladin8
3237 posts
paladin8
#29 h  Jan 19, 2007, 2:06 AM • 2 Y
Y by Adventure10, Mango247
Ubemaya wrote:
Can I turn it in today?

I didn't hear about it until today...

and if I can't, can I just submit it to see what score I got?

Sure, but I won't update the statistics. You can just check your answers in the other thread anyway.
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ghjk
858 posts
ghjk
#30 h  Jan 20, 2008, 6:22 AM • 2 Y
Y by Adventure10, Mango247
Sorry for my reviving this old thread!But can anyone post the answer key of this test since I need to see where my score is?? I need to see the solution of 1 or 2 problems in this test(23 and another).
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nitish
8 posts
nitish
#31 h  Feb 9, 2008, 6:03 AM • 4 Y
Y by Adventure10, Mango247, Mango247, Mango247
Could you give the answers to the test.
I am just practicing for the AMC 12.
My email is
Aggarwal.nitish@gmail.com

Thanks
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Ignite168
1902 posts
Ignite168
#32 h  Feb 11, 2008, 7:29 AM • 1 Y
Y by Adventure10
http://www.artofproblemsolving.com/Forum/viewtopic.php?t=129159

Now please stop bumping this topic.
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