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k a May Highlights and 2025 AoPS Online Class Information
jlacosta   0
Thursday at 11:16 PM
May is an exciting month! National MATHCOUNTS is the second week of May in Washington D.C. and our Founder, Richard Rusczyk will be presenting a seminar, Preparing Strong Math Students for College and Careers, on May 11th.

Are you interested in working towards MATHCOUNTS and don’t know where to start? We have you covered! If you have taken Prealgebra, then you are ready for MATHCOUNTS/AMC 8 Basics. Already aiming for State or National MATHCOUNTS and harder AMC 8 problems? Then our MATHCOUNTS/AMC 8 Advanced course is for you.

Summer camps are starting next month at the Virtual Campus in math and language arts that are 2 - to 4 - weeks in duration. Spaces are still available - don’t miss your chance to have an enriching summer experience. There are middle and high school competition math camps as well as Math Beasts camps that review key topics coupled with fun explorations covering areas such as graph theory (Math Beasts Camp 6), cryptography (Math Beasts Camp 7-8), and topology (Math Beasts Camp 8-9)!

Be sure to mark your calendars for the following upcoming events:
[list][*]May 9th, 4:30pm PT/7:30pm ET, Casework 2: Overwhelming Evidence — A Text Adventure, a game where participants will work together to navigate the map, solve puzzles, and win! All are welcome.
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[*]May 20th, 4:00pm PT/7:00pm ET, Mathcamp 2025 Qualifying Quiz Part 1 Math Jam, Problems 1 to 4, join the Canada/USA Mathcamp staff for this exciting Math Jam, where they discuss solutions to Problems 1 to 4 of the 2025 Mathcamp Qualifying Quiz!
[*]May 21st, 4:00pm PT/7:00pm ET, Mathcamp 2025 Qualifying Quiz Part 2 Math Jam, Problems 5 and 6, Canada/USA Mathcamp staff will discuss solutions to Problems 5 and 6 of the 2025 Mathcamp Qualifying Quiz![/list]
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0 replies
jlacosta
Thursday at 11:16 PM
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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IMO Genre Predictions
ohiorizzler1434   0
2 minutes ago
Everybody, with IMO upcoming, what are you predictions for the problem genres?


Personally I predict: predict
0 replies
1 viewing
ohiorizzler1434
2 minutes ago
0 replies
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Equal sum of digits
Fudicuehfosonrcjeong   0
23 minutes ago
Is it true that for any two positive integers a, b there exists a positive integer k such that s(ka)=s(kb), where s(n) is sum of digits in base 10?
0 replies
2 viewing
Fudicuehfosonrcjeong
23 minutes ago
0 replies
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Common tangent of mixtilinear incircles
CyclicISLscelesTrapezoid   3
N 29 minutes ago by Ilikeminecraft
Source: MOP 2020/1Z
Let $ABCD$ be a quadrilateral inscribed in circle $\Omega$. Circles $\omega_A$ and $\omega_D$ are drawn internally tangent to $\Omega$, such that $\omega_A$ is tangent to $\overline{AB}$ and $\overline{AC}$ while $\omega_D$ is tangent to $\overline{DB}$ and $\overline{DC}$. Prove that we can draw a line parallel to $\overline{AD}$ which is simultaneously tangent to both $\omega_A$ and $\omega_D$.
3 replies
1 viewing
CyclicISLscelesTrapezoid
Jan 6, 2023
Ilikeminecraft
29 minutes ago
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Construct
Pomegranat   2
N 35 minutes ago by Blackbeam999
Source: idk
Let \( p \) be a prime number. Prove that there exists a natural number \( n \) such that
\[ p \mid m^n - n. \]
2 replies
Pomegranat
Apr 30, 2025
Blackbeam999
35 minutes ago
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square root problem
kjhgyuio   2
N 40 minutes ago by wh0nix
........
2 replies
kjhgyuio
2 hours ago
wh0nix
40 minutes ago
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Almost Squarefree Integers
oVlad   4
N an hour ago by HeshTarg
Source: Romania Junior TST 2025 Day 1 P1
A positive integer $n\geqslant 3$ is almost squarefree if there exists a prime number $p\equiv 1\bmod 3$ such that $p^2\mid n$ and $n/p$ is squarefree. Prove that for any almost squarefree positive integer $n$ the ratio $2\sigma(n)/d(n)$ is an integer.
4 replies
oVlad
Apr 12, 2025
HeshTarg
an hour ago
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A nice and easy gem off of StackExchange
NamelyOrange   2
N 2 hours ago by Royal_mhyasd
Source: https://math.stackexchange.com/questions/3818796/
Define $S$ as the set of all numbers of the form $2^i5^j$ for some nonnegative $i$ and $j$. Find (with proof) all pairs $(m,n)$ such that $m,n\in S$ and $m-n=1$.


Rephrased: Solve $2^a5^b-2^c5^d=1$ over $(\mathbb{N}_0)^4$, and prove that your solution(s) is/are the only one(s).
2 replies
NamelyOrange
Yesterday at 8:13 PM
Royal_mhyasd
2 hours ago
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Comics and triangles in perspective
srirampanchapakesan   1
N 2 hours ago by ohiorizzler1434
Source: Own
Let a conic intersect the sides BC, CA, AB of triangle ABC at A1,A2,B1,B2,C1,C2.

T1 is the triangle formed by A1B2, B1C2, and C1A2.

T2 is the triangle formed by A2B1, B2C1 and C2A1.

Prove that the triangles ABC, T1 and T2 are pair-wise in perspective.

Also prove that all three centers of perspective coincide.
1 reply
srirampanchapakesan
3 hours ago
ohiorizzler1434
2 hours ago
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Integer a_k such that b - a^n_k is divisible by k
orl   70
N 2 hours ago by Aiden-1089
Source: IMO Shortlist 2007, N2, Ukrainian TST 2008 Problem 10
Let $b,n > 1$ be integers. Suppose that for each $k > 1$ there exists an integer $a_k$ such that $b - a^n_k$ is divisible by $k$. Prove that $b = A^n$ for some integer $A$.

Author: Dan Brown, Canada
70 replies
orl
Jul 13, 2008
Aiden-1089
2 hours ago
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minimum of \sqrt{\frac{a}{b(3a+2)}}+\sqrt{\frac{b}{a(3b+2)}}
parmenides51   10
N 2 hours ago by Tomilovedoingmath
Source: JBMO Shortlist 2017 A2
Let $a$ and $b$ be positive real numbers such that $3a^2 + 2b^2 = 3a + 2b$. Find the minimum value of $A =\sqrt{\frac{a}{b(3a+2)}} + \sqrt{\frac{b}{a(2b+3)}} $
10 replies
parmenides51
Jul 25, 2018
Tomilovedoingmath
2 hours ago
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inequalities
Cobedangiu   1
N 3 hours ago by xytunghoanh
$a,b,c>0$ and $\sum ab=\dfrac{1}{3}$. Prove that:
$\sum \dfrac{1}{a^2-bc+1}\le 3$
1 reply
Cobedangiu
3 hours ago
xytunghoanh
3 hours ago
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this geo is scarier than the omega variant
AwesomeYRY   10
N 3 hours ago by GrantStar
Source: TSTST 2021/6
Triangles $ABC$ and $DEF$ share circumcircle $\Omega$ and incircle $\omega$ so that points $A,F,B,D,C,$ and $E$ occur in this order along $\Omega$. Let $\Delta_A$ be the triangle formed by lines $AB,AC,$ and $EF,$ and define triangles $\Delta_B, \Delta_C, \ldots, \Delta_F$ similarly. Furthermore, let $\Omega_A$ and $\omega_A$ be the circumcircle and incircle of triangle $\Delta_A$, respectively, and define circles $\Omega_B, \omega_B, \ldots, \Omega_F, \omega_F$ similarly.

(a) Prove that the two common external tangents to circles $\Omega_A$ and $\Omega_D$ and the two common external tangents to $\omega_A$ and $\omega_D$ are either concurrent or pairwise parallel.

(b) Suppose that these four lines meet at point $T_A$, and define points $T_B$ and $T_C$ similarly. Prove that points $T_A,T_B$, and $T_C$ are collinear.

Nikolai Beluhov
10 replies
AwesomeYRY
Dec 13, 2021
GrantStar
3 hours ago
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3-var inequality
sqing   1
N 3 hours ago by sqing
Source: Own
Let $ a,b,c\geq 0 ,a+b+c =4. $ Prove that
$$a +ab^2 +ab^2c \leq\frac{33}{4}+2\sqrt 2$$$$a +ab^2 +abc \leq \frac{2(100+13\sqrt {13})}{27}$$$$a +a^2b + a b^2c^3\leq \frac{2(82+19\sqrt {19})}{27}$$
1 reply
sqing
3 hours ago
sqing
3 hours ago
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Hard to approach it !
BogG   128
N 3 hours ago by alexanderchew
Source: Swiss Imo Selection 2006
Let $\triangle ABC$ be an acute-angled triangle with $AB \not= AC$. Let $H$ be the orthocenter of triangle $ABC$, and let $M$ be the midpoint of the side $BC$. Let $D$ be a point on the side $AB$ and $E$ a point on the side $AC$ such that $AE=AD$ and the points $D$, $H$, $E$ are on the same line. Prove that the line $HM$ is perpendicular to the common chord of the circumscribed circles of triangle $\triangle ABC$ and triangle $\triangle ADE$.
128 replies
BogG
May 25, 2006
alexanderchew
3 hours ago
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Functionnal equation
Rayanelba   1
N Apr 30, 2025 by Mrcuberoot
Source: Own
Find all functions $f:\mathbb{R}_{>0}\to \mathbb{R}_{>0}$ that verify the following equation for all $x,y\in \mathbb{R}_{>0}$:
$f(x+yf(x))+f(\frac{x}{y})=\frac{x}{y}+f(x+xy)$
1 reply
Rayanelba
Apr 30, 2025
Mrcuberoot
Apr 30, 2025
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Functionnal equation
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Reveal topic tags
algebra
functional equation
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Source: Own
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Rayanelba
14 posts
Rayanelba
#1 h  Apr 30, 2025, 4:10 PM
Y by
Find all functions $f:\mathbb{R}_{>0}\to \mathbb{R}_{>0}$ that verify the following equation for all $x,y\in \mathbb{R}_{>0}$:
$f(x+yf(x))+f(\frac{x}{y})=\frac{x}{y}+f(x+xy)$
This post has been edited 2 times. Last edited by Rayanelba, Apr 30, 2025, 7:25 PM
Reason: Typo
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The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
Mrcuberoot
27 posts
Mrcuberoot
#2 h  Apr 30, 2025, 6:27 PM • 2 Y
Y by Rayanelba, ATM_
Unsolvable probably
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