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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!
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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
J
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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
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MOHS for Day 1
MajesticCheese   25
N 3 minutes ago by Mathandski
What is your opinion for MOHS for day 1?

JMO 1:
JMO 2/AMO 1:
JMO 3:
AMO 2:
AMO 3:
25 replies
+1 w
MajesticCheese
Yesterday at 3:15 PM
Mathandski
3 minutes ago
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funny title placeholder
pikapika007   43
N 6 minutes ago by VulcanForge
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.
43 replies
+3 w
pikapika007
5 hours ago
VulcanForge
6 minutes ago
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usamOOK geometry
KevinYang2.71   46
N 12 minutes ago by hgomamogh
Source: USAMO 2025/4, USAJMO 2025/5
Let $H$ be the orthocenter of acute triangle $ABC$, let $F$ be the foot of the altitude from $C$ to $AB$, and let $P$ be the reflection of $H$ across $BC$. Suppose that the circumcircle of triangle $AFP$ intersects line $BC$ at two distinct points $X$ and $Y$. Prove that $C$ is the midpoint of $XY$.
46 replies
+1 w
KevinYang2.71
5 hours ago
hgomamogh
12 minutes ago
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2025 USA(J)MO Cutoff Predictions
KevinChen_Yay   40
N 19 minutes ago by Jack_w
What do y'all think JMO winner and MOP cuts will be?

(Also, to satisfy the USAMO takers; what about the bronze, silver, gold, green mop, blue mop, black mop?)
40 replies
+4 w
KevinChen_Yay
5 hours ago
Jack_w
19 minutes ago
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Inequality and function
srnjbr   0
43 minutes ago
Find all f:R--R such that for all x,y, yf(x)+f(y)>=f(xy)
0 replies
srnjbr
43 minutes ago
0 replies
J
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Inspired by hunghd8
sqing   1
N an hour ago by sqing
Source: Own
Let $ a,b,c\geq 0 $ and $ a+b+c\geq 2+abc . $ Prove that
$$a^2+b^2+c^2- abc\geq \frac{7}{4}$$$$a^2+b^2+c^2-2abc \geq 1$$$$a^2+b^2+c^2- \frac{1}{2}abc\geq \frac{31}{16}$$$$a^2+b^2+c^2- \frac{8}{5}abc\geq \frac{34}{25}$$
1 reply
sqing
an hour ago
sqing
an hour ago
J
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Assisted perpendicular chasing
sarjinius   2
N an hour ago by chisa36
Source: Philippine Mathematical Olympiad 2025 P7
In acute triangle $ABC$ with circumcenter $O$ and orthocenter $H$, let $D$ be an arbitrary point on the circumcircle of triangle $ABC$ such that $D$ does not lie on line $OB$ and that line $OD$ is not parallel to line $BC$. Let $E$ be the point on the circumcircle of triangle $ABC$ such that $DE$ is perpendicular to $BC$, and let $F$ be the point on line $AC$ such that $FA = FE$. Let $P$ and $R$ be the points on the circumcircle of triangle $ABC$ such that $PE$ is a diameter, and $BH$ and $DR$ are parallel. Let $M$ be the midpoint of $DH$.
(a) Show that $AP$ and $BR$ are perpendicular.
(b) Show that $FM$ and $BM$ are perpendicular.
2 replies
sarjinius
Mar 9, 2025
chisa36
an hour ago
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Find min
hunghd8   4
N an hour ago by imnotgoodatmathsorry
Let $a,b,c$ be nonnegative real numbers such that $ a+b+c\geq 2+abc $. Find min
$$P=a^2+b^2+c^2.$$
4 replies
hunghd8
5 hours ago
imnotgoodatmathsorry
an hour ago
J
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Prime for square numbers
giangtruong13   1
N 2 hours ago by shanelin-sigma
Source: City’s Specialized Math Examination
Given that $a,b$ are natural numbers satisfy that: $\frac{a^3}{a+b}$ and $\frac{b^3}{a+b}$ are prime numbers. Prove that $$a^2+3ab+3a+b+1$$is a perfect squared number
1 reply
giangtruong13
2 hours ago
shanelin-sigma
2 hours ago
J
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Inspired by hunghd8
sqing   0
2 hours ago
Source: Own
Let $ a,b,c\geq 0 $ and $ a+b+c\geq 2+abc . $ Prove that
$$a^2+b^2+c^2-\frac{1}{2}a^2b^2c^2\geq 2$$$$a^2+b^2+c^2-abc-\frac{1}{2}a^2b^2c^2\geq \frac{3}{2}$$$$a^2+b^2+c^2- \frac{19}{10}abc-\frac{1}{2}a^2b^2c^2\geq -\frac{12}{25}$$$$a^2+b^2+c^2- \frac{3}{2}abc-\frac{1}{2}a^2b^2c^2\geq \frac{17\sqrt{17}-71}{16}$$
0 replies
sqing
2 hours ago
0 replies
J
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Interesting inequality
sqing   5
N 2 hours ago by sqing
Source: Own
Let $ a,b >0. $ Prove that
$$ \frac{1}{\frac{a}{a+b}+\frac{a}{2b}} +\frac{1}{\frac{b}{a+b}+\frac{1}{2}} +\frac{a}{2b} \geq \frac{5}{2} $$
5 replies
sqing
Feb 26, 2025
sqing
2 hours ago
J
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sum of divisors nt
Soupboy0   0
2 hours ago
Source: own
Let $\epsilon(n)$ denote the sum of the sum of the factors of all positive $\mathbb Z \le n$, for example, $\epsilon(5) $ is the sum of the factors of $5$ added to the sum of the factors of $4$ and so on until the sum of the factors of $1$, which would be $(1+5)+(1+2+4)+(1+3)+(1+2)+(1) = 21$. Let $M(n)$ denote $\sum_{i=1}^{n} n \pmod{i}$. Show that $\epsilon(n) + M(n) = n^2$ or find a counterexample
0 replies
Soupboy0
2 hours ago
0 replies
J
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euler-totient function
Laan   2
N 2 hours ago by Laan
Proof that there are infinitely many positive integers $n$ such that
$\varphi(n)<\varphi(n+1)<\varphi(n+2)$
2 replies
Laan
Today at 7:13 AM
Laan
2 hours ago
J
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2 var inquality
sqing   5
N 3 hours ago by sqing
Source: Own
Let $ a,b $ be nonnegative real numbers such that $ a^2+ab+b^2+a+b=1. $ Prove that
$$ (ab+1)(a+b)\leq \frac{ 20}{27} $$$$ (ab+1)(a+b-1)\leq - \frac{ 10}{27} $$Let $ a,b $ be nonnegative real numbers such that $ a^2+b^2+a+b=1. $ Prove that
$$ (ab+1)(a+b)\leq \frac{ 5\sqrt 3-7}{2} $$$$ (ab+1)(a+b-1)\leq 3\sqrt 3- \frac{ 11}{2} $$
5 replies
sqing
Yesterday at 3:00 PM
sqing
3 hours ago
J
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J
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AMC 10.........
BAM10   15
N Mar 18, 2025 by jkim0656
I'm in 8th grade and have never taken the AMC 10. I am currently in alg2. I have scored 20 on AMC 8 this year and 34 on the chapter math counts last year. Can I qualify for AIME. Also what should I practice AMC 10 next year?
15 replies
BAM10
Mar 2, 2025
jkim0656
Mar 18, 2025
J
AMC 10.........
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Reveal topic tags
AMC 10
AMC 8
MATHCOUNTS
AIME
L
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BAM10
68 posts
BAM10
#1 h  Mar 2, 2025, 8:02 PM
Y by
I'm in 8th grade and have never taken the AMC 10. I am currently in alg2. I have scored 20 on AMC 8 this year and 34 on the chapter math counts last year. Can I qualify for AIME. Also what should I practice AMC 10 next year?
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orangebear
611 posts
orangebear
#2 h  Mar 2, 2025, 8:04 PM
Y by
Yeah you can last year I got a 19 on AMC and a 31 on mathcounts chapter and I qualified for AIME.
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CYW
326 posts
CYW
#3 h  Mar 2, 2025, 9:06 PM
Y by
Dunno, opposite way for me. I got 80-something on AMC 10 (cutoff mid 90's) and got 37 on MATHCOUNTS chapter
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Airbus320-214
77 posts
Airbus320-214
#4 h  Mar 3, 2025, 3:07 AM
Y by
Practice past problems of amc 10/12
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nxchman
21 posts
nxchman
#5 h  Mar 3, 2025, 9:09 PM
Y by
BAM10 wrote:
I'm in 8th grade and have never taken the AMC 10. I am currently in alg2. I have scored 20 on AMC 8 this year and 34 on the chapter math counts last year. Can I qualify for AIME. Also what should I practice AMC 10 next year?

Im in the same boat lol. Im in 8th grade and I never took amc 10, but this year I got 22 on amc 8.
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iwillregretthisnamelater
6 posts
iwillregretthisnamelater
#6 h  Mar 18, 2025, 1:59 AM
Y by
I’m in 6th grade and I got 20 on amc 8 and 38 on chapter and i flunked the amc 10 so hard
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sadas123
1065 posts
sadas123
#7 h  Mar 18, 2025, 2:04 AM
Y by
iwillregretthisnamelater wrote:
I’m in 6th grade and I got 20 on amc 8 and 38 on chapter and i flunked the amc 10 so hard

Same except I am a 6th grader that got 24 on AMC 8 and a 37 on mathcounts chapter :(
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jb2015007
1712 posts
jb2015007
#8 h  Mar 18, 2025, 2:09 AM
Y by
orangebear wrote:
Yeah you can last year I got a 19 on AMC and a 31 on mathcounts chapter and I qualified for AIME.

bruh i got a 51 on AMC 10 and got a 35 on mc chapter
(im better now relax im mocking 90+)
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ChickensEatGrass
26 posts
ChickensEatGrass
#9 h  Mar 18, 2025, 2:19 AM
Y by
I'm an 8th grader and I got 25 on amc8 but only 40 on chapter, I made aime barely this year but I got like problem 4 wrong on 10a :wallbash_red:
so yes with your stats you have a decent chance, just study more and do past mocks, you can find them here on aops.
try to aim for at least 100. This year's cutoff for 10a was really low (94.5) but most years it's higher.
because you are in alg2, I'd recommend doing some geometry because there are several of those problems. maybe also start trig because they can provide faster solutions to them. but alg2 is a good start.
And make sure to not make sillies!!!!!!!!!! but I cant rlly say anything about that because i myself make 100000000 sillies every day :whistling:
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giratina3
436 posts
giratina3
#10 h  Mar 18, 2025, 11:35 AM
Y by
I’m somebody who got 41 on chapter and 21 on AMC8 but didn’t qualify for AIME :stretcher:
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hashbrown2009
111 posts
hashbrown2009
#11 h  Mar 18, 2025, 1:54 PM
Y by
Honestly it depends
I qualified for AIME in 5th grade (9th grade now) with 106.5
but that year I got like 16 on AMC8 lol I sold
also I pre-prepped for MathCounts and did mocks
averaged like 36-40
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Andyluo
856 posts
Andyluo
#12 h  Mar 18, 2025, 4:23 PM
Y by
Both completely different skill sets

my scores last year were

AMC 8: 17
chapter: 41 (My MATHCOUNTS skills were more developed)
AMC 10: 81

This year:

AMC 8: 21
Chapter: 43
AMC 10: 135

imo just take mocks + learn the theory from aops
mathdash good too
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BAM10
68 posts
BAM10
#13 h  Mar 18, 2025, 9:39 PM
Y by
thx for the help. I have taken a couple mocks.

2020 10a: 84.5
2020 10b: 99
2021 10a: 87.5

Im finding that I can the first 10-15 pretty easily but I silly a lot a can't get many after #15. How can I help these problems?
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Pengu14
427 posts
Pengu14
#14 h  Mar 18, 2025, 10:10 PM
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BAM10 wrote:
thx for the help. I have taken a couple mocks.

2020 10a: 84.5
2020 10b: 99
2021 10a: 87.5

Im finding that I can the first 10-15 pretty easily but I silly a lot a can't get many after #15. How can I help these problems?

Can you solve the problems with unlimited time? If not, you should probably read AOPS vol 1 since you might be lacking theory.
This post has been edited 1 time. Last edited by Pengu14, Mar 18, 2025, 10:11 PM
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gavinhaominwang
73 posts
gavinhaominwang
#15 h  Mar 18, 2025, 10:23 PM
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If you are talking about qualifying for aime this year, anyone that can take the test can qualify for aime. They just have to work hard.
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jkim0656
297 posts
jkim0656
#16 h  Mar 18, 2025, 10:46 PM
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lol im in 7thn but i also got 34 on chapter and 20 on the amc8 loll
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