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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]
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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
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Olympiad book reading help
Enes040612   1
N a few seconds ago by haohao6688
Hello, does anyone else struggle with reading math olympiad books or am I just the only one? Whenever i try to study any different books I often get confused or overwhelmed very easily. This makes the process of studying very hard for me. Do you guys have any tips, or techniques you used? Any good videos you know?
1 reply
Enes040612
Jan 4, 2025
haohao6688
a few seconds ago
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Sums Of Polynomials
oVlad   16
N 9 minutes ago by N3bula
Source: IZhO 2022 Day 2 Problem 5
A polynomial $f(x)$ with real coefficients of degree greater than $1$ is given. Prove that there are infinitely many positive integers which cannot be represented in the form \[f(n+1)+f(n+2)+\cdots+f(n+k)\]where $n$ and $k$ are positive integers.
16 replies
+1 w
oVlad
Feb 18, 2022
N3bula
9 minutes ago
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Loop of Logarithms
scls140511   11
N 10 minutes ago by ohiorizzler1434
Source: 2024 China Round 1 (Gao Lian)
Round 1

1 Real number $m>1$ satisfies $\log_9 \log_8 m =2024$. Find the value of $\log_3 \log_2 m$.
11 replies
scls140511
Sep 8, 2024
ohiorizzler1434
10 minutes ago
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Looooong Geo Finale for Day 2
AlperenINAN   1
N 13 minutes ago by sami1618
Source: Turkey TST 2025 P6
Let $ABC$ be a scalene triangle with incenter $I$ and incircle $\omega$. Let the tangency points of $\omega$ to $BC,AC\text{ and } AB$ be $D,E,F$ respectively. Let the line $EF$ intersect the circumcircle of $ABC$ at the points $G, H$. Assume that $E$ lies between the points $F$ and $G$. Let $\Gamma$ be a circle that passes through $G$ and $H$ and that is tangent to $\omega$ at the point $M$ which lies on different semi-planes with $D$ with respect to the line $EF$. Let $\Gamma$ intersect $BC$ at points $K$ and $L$ and let the second intersection point of the circumcircle of $ABC$ and the circumcircle of $AKL$ be $N$. Prove that the intersection point of $NM$ and $AI$ lies on the circumcircle of $ABC$ if and only if the intersection point of $HB$ and $GC$ lies on $\Gamma$.
1 reply
1 viewing
AlperenINAN
Yesterday at 6:44 AM
sami1618
13 minutes ago
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Greece JBMO TST
ultralako   24
N 20 minutes ago by ali123456
Source: Greece JBMO TST Problem 4
Find all positive integers $x,y,z$ with $z$ odd, which satisfy the equation:

$$2018^x=100^y + 1918^z$$
24 replies
ultralako
Apr 22, 2018
ali123456
20 minutes ago
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f(x^2 + f(y)) = y + (f(x))^2
orl   55
N an hour ago by KAME06
Source: IMO 1992, Day 1, Problem 2
Let $\,{\mathbb{R}}\,$ denote the set of all real numbers. Find all functions $\,f: {\mathbb{R}}\rightarrow {\mathbb{R}}\,$ such that \[ f\left( x^{2}+f(y)\right) =y+\left( f(x)\right) ^{2}\hspace{0.2in}\text{for all}\,x,y\in \mathbb{R}. \]
55 replies
1 viewing
orl
Nov 11, 2005
KAME06
an hour ago
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Cool Number Theory
Fermat_Fanatic108   8
N an hour ago by BR1F1SZ
For an integer with 5 digits $n=abcde$ (where $a, b, c, d, e$ are the digits and $a\neq 0$) we define the \textit{permutation sum} as the value $$bcdea+cdeab+deabc+eabcd$$For example the permutation sum of 20253 is $$02532+25320+53202+32025=113079$$Let $m$ and $n$ be two fivedigit integers with the same permutation sum.
Prove that $m=n$.
8 replies
Fermat_Fanatic108
Today at 1:41 PM
BR1F1SZ
an hour ago
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@@hard question
o.k.oo   0
an hour ago
A total of 3300 handshakes were made at a party attended by 600 people. It was observed
that the total number of handshakes among any 300 people at the party is at least N. Find
the largest possible value for N.
0 replies
o.k.oo
an hour ago
0 replies
J
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Max amount of equal numbers among (a_i^2 + a_j^2)/(a_i + a_j)
mshtand1   2
N an hour ago by mshtand1
Source: Ukrainian Mathematical Olympiad 2025. Day 2, Problem 9.8
Given $2025$ pairwise distinct positive integer numbers \(a_1, a_2, \ldots, a_{2025}\), find the maximum possible number of equal numbers among the fractions of the form
\[ \frac{a_i^2 + a_j^2}{a_i + a_j} \]
Proposed by Mykhailo Shtandenko
2 replies
mshtand1
Mar 14, 2025
mshtand1
an hour ago
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Incenter geometry with parallel lines
nAalniaOMliO   2
N 2 hours ago by nAalniaOMliO
Source: Belarusian MO 2023
Let $\omega$ be the incircle of triangle $ABC$. Line $l_b$ is parallel to side $AC$ and tangent to $\omega$. Line $l_c$ is parallel to side $AB$ and tangent to $\omega$. It turned out that the intersection point of $l_b$ and $l_c$ lies on circumcircle of $ABC$
Find all possible values of $\frac{AB+AC}{BC}$
2 replies
nAalniaOMliO
Apr 16, 2024
nAalniaOMliO
2 hours ago
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Problem about Euler's function
luutrongphuc   3
N 2 hours ago by ishan.panpaliya
Prove that for every integer $n \ge 5$, we have:
$$ 2^{n^2+3n-13} \mid \phi \left(2^{2^{n}}-1 \right)$$
3 replies
luutrongphuc
Today at 4:23 PM
ishan.panpaliya
2 hours ago
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Function equation
Dynic   3
N 3 hours ago by Filipjack
Find all function $f:\mathbb{Z}\to\mathbb{Z}$ satisfy all conditions below:
i) $f(n+1)>f(n)$ for all $n\in \mathbb{Z}$
ii) $f(-n)=-f(n)$ for all $n\in \mathbb{Z}$
iii) $f(a^3+b^3+c^3+d^3)=f^3(a)+f^3(b)+f^3(c)+f^3(d)$ for all $n\in \mathbb{Z}$
3 replies
Dynic
6 hours ago
Filipjack
3 hours ago
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solve in positive integers: 3 \cdot 2^x +4 =n^2
parmenides51   3
N 3 hours ago by ali123456
Source: Greece JBMO TST 2019 p2
Find all pairs of positive integers $(x,n) $ that are solutions of the equation $3 \cdot 2^x +4 =n^2$.
3 replies
parmenides51
Apr 29, 2019
ali123456
3 hours ago
J
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2^a + 3^b + 1 = 6^c
togrulhamidli2011   3
N 4 hours ago by Tamam
Find all positive integers (a, b, c) such that:

\[ 2^a + 3^b + 1 = 6^c \]
3 replies
togrulhamidli2011
Mar 16, 2025
Tamam
4 hours ago
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unnecessary wrapped FE on Q
iStud   1
N Yesterday at 6:11 AM by jasperE3
Source: Monthly Contest KTOM March 2025 P3 Essay
Find all functions $f:\mathbb{Q}\to\mathbb{Q}$ such that
\[f(f(f(\frac{x+y}{2}))+x+y)=f(x)+f(y)+f(\frac{x+y}{2})\]for all rational numbers $x,y$.

Hint
1 reply
iStud
Yesterday at 3:56 AM
jasperE3
Yesterday at 6:11 AM
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unnecessary wrapped FE on Q
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Reveal topic tags
function
algebra
Cauchy functional equation
wrapped
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Source: Monthly Contest KTOM March 2025 P3 Essay
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
iStud
257 posts
iStud
#1 h  Yesterday at 3:56 AM
Y by
Find all functions $f:\mathbb{Q}\to\mathbb{Q}$ such that
\[f(f(f(\frac{x+y}{2}))+x+y)=f(x)+f(y)+f(\frac{x+y}{2})\]for all rational numbers $x,y$.

Hint
This post has been edited 1 time. Last edited by iStud, Yesterday at 4:00 AM
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
jasperE3
11100 posts
jasperE3
#2 h  Yesterday at 6:11 AM
Y by
iStud wrote:
Find all functions $f:\mathbb{Q}\to\mathbb{Q}$ such that
\[f(f(f(\frac{x+y}{2}))+x+y)=f(x)+f(y)+f(\frac{x+y}{2})\]for all rational numbers $x,y$.

Hint

Let $g:\mathbb Q\to\mathbb Q$ be defined by $g(x)=f\left(f\left(f\left(\frac x2\right)\right)+x\right)-f\left(\frac x2\right)$, the equation rewrites as $P(x,y):g(x+y)=f(x)+f(y)$. $P(x+y,0)$ gives $g(x+y)=f(x+y)+f(0)$ so $f(x+y)+f(0)=f(x)+f(y)$, finishing is standard.
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