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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.

Are you ready to level up with Olympiad training? Registration is open with early bird pricing available for our WOOT programs: MathWOOT (Levels 1 and 2), CodeWOOT, PhysicsWOOT, and ChemWOOT. What is WOOT? WOOT stands for Worldwide Online Olympiad Training and is a 7-month high school math Olympiad preparation and testing program that brings together many of the best students from around the world to learn Olympiad problem solving skills. Classes begin in September!

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]
Our full course list for upcoming classes is below:
All classes run 7:30pm-8:45pm ET/4:30pm - 5:45pm PT unless otherwise noted.

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0 replies
jlacosta
Mar 2, 2025
0 replies
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
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
2 var inquality
sqing   4
N an hour ago by sqing
Source: Own
Let $ a ,  b\geq 0 $ and $ \frac{1}{a^2+1}+\frac{1}{b^2+1}\le   \frac{3}{2}. $ Show that$$ a+b+ab\geq1$$Let $ a ,  b\geq 0 $ and $ \frac{1}{a^2+1}+\frac{1}{b^2+1}\le   \frac{5}{6}. $ Show that$$ a+b+ab\geq2$$
4 replies
+1 w
sqing
Today at 4:06 AM
sqing
an hour ago
Functional inequality on N
BartSimpsons   21
N an hour ago by Tony_stark0094
Source: European Mathematical Cup 2017 Problem 1
Find all functions $f:\mathbb{N}\rightarrow \mathbb{N}$ such that the inequality $$f(x)+yf(f(x))\le x(1+f(y))$$holds for all positive integers $x, y$.

Proposed by Adrian Beker.
21 replies
BartSimpsons
Dec 27, 2017
Tony_stark0094
an hour ago
A colouring game on a rectangular frame
Tintarn   0
an hour ago
Source: Bundeswettbewerb Mathematik 2025, Round 1 - Problem 4
For integers $m,n \ge 3$ we consider a $m \times n$ rectangular frame, consisting of the $2m+2n-4$ boundary squares of a $m \times n$ rectangle.

Renate and Erhard play the following game on this frame, with Renate to start the game. In a move, a player colours a rectangular area consisting of a single or several white squares. If there are any more white squares, they have to form a connected region. The player who moves last wins the game.

Determine all pairs $(m,n)$ for which Renate has a winning strategy.
0 replies
Tintarn
an hour ago
0 replies
Find the value
sqing   5
N an hour ago by sqing
Source: Own
Let $a,b,c$ be distinct real numbers such that $ \frac{a^2}{(a-b)^2}+ \frac{b^2}{(b-c)^2}+ \frac{c^2}{(c-a)^2} =1. $ Find the value of $\frac{a}{a-b}+ \frac{b}{b-c}+ \frac{c}{c-a}.$
Let $a,b,c$ be distinct real numbers such that $\frac{a^2}{(b-c)^2}+ \frac{b^2}{(c-a)^2}+ \frac{c^2}{(a-b)^2}=2. $ Find the value of $\frac{a}{b-c}+ \frac{b}{c-a}+ \frac{c}{a-b}.$
Let $a,b,c$ be distinct real numbers such that $\frac{(a+b)^2}{(a-b)^2}+ \frac{(b+c)^2}{(b-c)^2}+ \frac{(c+a)^2}{(c-a)^2}=2. $ Find the value of $\frac{a+b}{a-b}+\frac{b+c}{b-c}+ \frac{c+a}{c-a}.$
5 replies
sqing
Today at 5:02 AM
sqing
an hour ago
A touching question on perpendicular lines
Tintarn   0
an hour ago
Source: Bundeswettbewerb Mathematik 2025, Round 1 - Problem 3
Let $k$ be a semicircle with diameter $AB$ and midpoint $M$. Let $P$ be a point on $k$ different from $A$ and $B$.

The circle $k_A$ touches $k$ in a point $C$, the segment $MA$ in a point $D$, and additionally the segment $MP$. The circle $k_B$ touches $k$ in a point $E$ and additionally the segments $MB$ and $MP$.

Show that the lines $AE$ and $CD$ are perpendicular.
0 replies
Tintarn
an hour ago
0 replies
The last nonzero digit of factorials
Tintarn   0
an hour ago
Source: Bundeswettbewerb Mathematik 2025, Round 1 - Problem 2
For each integer $n \ge 2$ we consider the last digit different from zero in the decimal expansion of $n!$. The infinite sequence of these digits starts with $2,6,4,2,2$. Determine all digits which occur at least once in this sequence, and show that each of those digits occurs in fact infinitely often.
0 replies
Tintarn
an hour ago
0 replies
Fridolin just can't get enough from jumping on the number line
Tintarn   0
an hour ago
Source: Bundeswettbewerb Mathematik 2025, Round 1 - Problem 1
Fridolin the frog jumps on the number line: He starts at $0$, then jumps in some order on each of the numbers $1,2,\dots,9$ exactly once and finally returns with his last jump to $0$. Can the total distance he travelled with these $10$ jumps be a) $20$, b) $25$?
0 replies
Tintarn
an hour ago
0 replies
D1016 : A strange result about the palindrom polynomials
Dattier   0
an hour ago
Source: les dattes à Dattier
Let $Q\in \{-1,1,0\}[x]$ with $Q(1)=0$.

Is it true that $\exists Q \in \mathbb Z[x]$ palindrom with $Q | P$ ?
0 replies
Dattier
an hour ago
0 replies
EMC last problem
GreekIdiot   1
N an hour ago by Tintarn
Source: EMC 2024 P4, Ioannis Galamatis
Find all functions $f: \mathbb{R_+} \rightarrow \mathbb{R_+}$ such that $f(x+yf(x))=xf(y+1) \: \forall\: x, \:y \in \mathbb{R_+}$.
Note: With the symbol $\mathbb{R_+}$ we denote the set of positive real numbers.
1 reply
GreekIdiot
Yesterday at 7:02 PM
Tintarn
an hour ago
Functional equation with a parameter
Tintarn   8
N an hour ago by NicoN9
Source: Baltic Way 2024, Problem 1
Let $\alpha$ be a non-zero real number. Find all functions $f: \mathbb{R}\to\mathbb{R}$ such that
\[
xf(x+y)=(x+\alpha y)f(x)+xf(y)
\]for all $x,y\in\mathbb{R}$.
8 replies
Tintarn
Nov 16, 2024
NicoN9
an hour ago
Writing Problem Extension
WildFitBrain   5
N Yesterday at 7:00 PM by bpan2021
I already submitted an extension but I cannot edit it because I submitted an unfinished solution. I have not viewed the solution.
5 replies
WildFitBrain
Yesterday at 6:12 PM
bpan2021
Yesterday at 7:00 PM
k Happy Pi Day!
greenplanet2050   5
N Saturday at 4:53 PM by Yihangzh
Happy Pi Day! $3.141592653589793238462643383279 50288419716939937510 5820974944 5923078164062862089986280348253421170679$

:D :D :D :D
5 replies
greenplanet2050
Mar 15, 2025
Yihangzh
Saturday at 4:53 PM
Error in Special AIME Seminar A solution
fermat_sLastAMC   1
N Mar 15, 2025 by MathPerson12321
The text in the following image (of the solution for problem #3 of the practice AIME of 4134 Special AIME Seminar A) should state that the positions of A and B are plotted on the vertical and time is plotted on the horizontal.

Where should I post these kinds of errors in the future?
1 reply
fermat_sLastAMC
Mar 15, 2025
MathPerson12321
Mar 15, 2025
Contest collection PDFs don't work when LaTeX is embedded within BBCode
Equinox8   5
N Mar 14, 2025 by jlacosta
This could very well be reported before, however a quick search did not find anything.

While embedding LaTeX commands within BBCode (like this: [i]text $\dfrac{1}{2}$ text[/i]) typically displays as intended within a forum, trying to render a contest collection using these commands breaks the PDF renderer.
5 replies
Equinox8
Feb 26, 2025
jlacosta
Mar 14, 2025
k Pi Day!!
SomeonecoolLovesMaths   66
N Mar 14, 2025 by LawofCosine
Happy $\pi$ day everyone!
66 replies
SomeonecoolLovesMaths
Mar 14, 2025
LawofCosine
Mar 14, 2025
Pi Day!!
G H J
G H BBookmark kLocked kLocked NReply
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liugra001
115 posts
#53
Y by
piiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii
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liugra001
115 posts
#54
Y by
SlyOwl45 wrote:
$\phantom{https://cdn.artofproblemsolving.com/attachments/6/2/4284d43d02ea9b30819a87eff72ca7f59a46a2.png}$

ha
This post has been edited 1 time. Last edited by liugra001, Mar 14, 2025, 7:14 PM
Reason: missed link
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derekwang2048
1188 posts
#55
Y by
pi, pie, and PIE
happy pi day!
Z Y
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GallopingUnicorn45
260 posts
#56
Y by
RandomeMids wrote:
PI!!!!!!!!!!!!!!!!!!!!!! (All i know is 3.141592653897

lol all I know is 3.1415
Z Y
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DhruvJha
731 posts
#57
Y by
3:14 on pi day
Z Y
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soumil2013
30 posts
#58
Y by
pi day yay
Z Y
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happymoose666
264 posts
#59
Y by
3.141592653589793238462643383279502884197
1693995820974944
is all I know
This post has been edited 1 time. Last edited by happymoose666, Mar 14, 2025, 8:48 PM
Z Y
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andersonouyang
48 posts
#60
Y by
3.1415926535 8979323846 2643383279 5028841971 6939937510
5820974944 5923078164 0628620899 8628034825 3421170679
8214808651 3282306647 0938446095 5058223172 5359408128
4811174502 8410270193 8521105559 6446229489 5493038196
4428810975 6659334461 2847564823 3786783165 2712019091
4564856692 3460348610 4543266482 1339360726 0249141273
7245870066 0631558817 4881520920 9628292540 9171536436
7892590360 0113305305 4882046652 1384146951 9415116094
3305727036 5759591953 0921861173 8193261179 3105118548
0744623799 6274956735 1885752724 8912279381 8301194912

9833673362 4406566430 8602139494 6395224737 1907021798
6094370277 0539217176 2931767523 8467481846 7669405132
0005681271 4526356082 7785771342 7577896091 7363717872
1468440901 2249534301 4654958537 1050792279 6892589235
4201995611 2129021960 8640344181 5981362977 4771309960
5187072113 4999999837 2978049951 0597317328 1609631859
5024459455 3469083026 4252230825 3344685035 2619311881
7101000313 7838752886 5875332083 8142061717 7669147303
5982534904 2875546873 1159562863 8823537875 9375195778
1857780532 1712268066 1300192787 6611195909 2164201989

3809525720 1065485863 2788659361 5338182796 8230301952
0353018529 6899577362 2599413891 2497217752 8347913151
5574857242 4541506959 5082953311 6861727855 8890750983
8175463746 4939319255 0604009277 0167113900 9848824012
8583616035 6370766010 4710181942 9555961989 4676783744
9448255379 7747268471 0404753464 6208046684 2590694912
9331367702 8989152104 7521620569 6602405803 8150193511
2533824300 3558764024 7496473263 9141992726 0426992279
6782354781 6360093417 2164121992 4586315030 2861829745
5570674983 8505494588 5869269956 9092721079 7509302955

3211653449 8720275596 0236480665 4991198818 3479775356
6369807426 5425278625 5181841757 4672890977 7727938000
8164706001 6145249192 1732172147 7235014144 1973568548
1613611573 5255213347 5741849468 4385233239 0739414333
4547762416 8625189835 6948556209 9219222184 2725502542
5688767179 0494601653 4668049886 2723279178 6085784383
8279679766 8145410095 3883786360 9506800642 2512520511
7392984896 0841284886 2694560424 1965285022 2106611863
0674427862 2039194945 0471237137 8696095636 4371917287
4677646575 7396241389 0865832645 9958133904 7802759009

9465764078 9512694683 9835259570 9825822620 5224894077
2671947826 8482601476 9909026401 3639443745 5305068203
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6868386894 2774155991 8559252459 5395943104 9972524680
8459872736 4469584865 3836736222 6260991246 0805124388
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4169486855 5848406353 4220722258 2848864815 8456028506
0168427394 5226746767 8895252138 5225499546 6672782398
6456596116 3548862305 7745649803 5593634568 1743241125

1507606947 9451096596 0940252288 7971089314 5669136867
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9009714909 6759852613 6554978189 3129784821 6829989487
2265880485 7564014270 4775551323 7964145152 3746234364
Z Y
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AlienGirl05
11040 posts
#61 • 1 Y
Y by At777
Happy $\pi$ Day!!!!! :)
Z Y
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mathbeast180
307 posts
#62
Y by
AlienGirl05 wrote:
Happy $\pi$ Day!!!!! :)
Z Y
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FiestyTiger82
695 posts
#63
Y by
3.14159265358
Z Y
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PatTheKing806
975 posts
#64
Y by
3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480
Z Y
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WoodBurnerB
3134 posts
#65 • 1 Y
Y by Exponent11
Happy Pi day!

This post has been edited 1 time. Last edited by WoodBurnerB, Mar 14, 2025, 9:25 PM
Z Y
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DhruvJha
731 posts
#66
Y by
Happy half Tau day!
Z Y
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LawofCosine
552 posts
#67 • 1 Y
Y by At777
I can remember 3.14159265358979323846 lol
Z Y
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