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k a May Highlights and 2025 AoPS Online Class Information
jlacosta   0
May 1, 2025
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)!

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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
May 1, 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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Substitution
JCE   3
N an hour ago by K124659
I've been working on this for about an hour or so, and I can't get this problem. I know the answer, but no idea on how to find it.
Please help?

2x-y^2=4
x^2+y=14
3 replies
JCE
May 27, 2006
K124659
an hour ago
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Something nice
KhuongTrang   34
N an hour ago by TNKT
Source: own
Problem. Given $a,b,c$ be non-negative real numbers such that $ab+bc+ca=1.$ Prove that

$$\sqrt{a+1}+\sqrt{b+1}+\sqrt{c+1}\le 1+2\sqrt{a+b+c+abc}.$$
34 replies
KhuongTrang
Nov 1, 2023
TNKT
an hour ago
J
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Problem 2, Grade 12th RMO Shortlist - Year 2002
sticknycu   3
N 2 hours ago by RobertRogo
Let $A \in M_2(C), A \neq O_2, A \neq I_2, n \in \mathbb{N}^*$ and $S_n = \{ X \in M_2(C) | X^n = A \}$.
Show:
a) $S_n$ with multiplication of matrixes operation is making an isomorphic-group structure with $U_n$.
b) $A^2 = A$.

Marian Andronache
3 replies
sticknycu
Jan 3, 2020
RobertRogo
2 hours ago
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Equation has no integer solution.
Learner94   34
N 2 hours ago by Ilikeminecraft
Source: INMO 2013
Let $a,b,c,d \in \mathbb{N}$ such that $a \ge b \ge c \ge d $. Show that the equation $x^4 - ax^3 - bx^2 - cx -d = 0$ has no integer solution.
34 replies
Learner94
Feb 3, 2013
Ilikeminecraft
2 hours ago
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Polynomial of Degree n
Brut3Forc3   20
N 3 hours ago by Ilikeminecraft
Source: 1975 USAMO Problem 3
If $ P(x)$ denotes a polynomial of degree $ n$ such that $ P(k)=\frac{k}{k+1}$ for $ k=0,1,2,\ldots,n$, determine $ P(n+1)$.
20 replies
Brut3Forc3
Mar 15, 2010
Ilikeminecraft
3 hours ago
J
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Really fun geometry problem
Sadigly   5
N 3 hours ago by GingerMan
Source: Azerbaijan Senior MO 2025 P6
In the acute triangle $ABC$ with $AB<AC$, the foot of altitudes from $A,B,C$ to the sides $BC,CA,AB$ are $D,E,F$, respectively. $H$ is the orthocenter. $M$ is the midpoint of segment $BC$. Lines $MH$ and $EF$ intersect at $K$. Let the tangents drawn to circumcircle $(ABC)$ from $B$ and $C$ intersect at $T$. Prove that $T;D;K$ are colinear
5 replies
Sadigly
Yesterday at 4:29 PM
GingerMan
3 hours ago
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Polynomials and powers
rmtf1111   27
N 3 hours ago by bjump
Source: RMM 2018 Day 1 Problem 2
Determine whether there exist non-constant polynomials $P(x)$ and $Q(x)$ with real coefficients satisfying
$$P(x)^{10}+P(x)^9 = Q(x)^{21}+Q(x)^{20}.$$
27 replies
rmtf1111
Feb 24, 2018
bjump
3 hours ago
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Equilateral triangle formed by circle and Fermat point
Mimii08   0
3 hours ago
Source: Heard from a friend
Hi! I found this interesting geometry problem and I would really appreciate help with the proof.

Let ABC be an acute triangle, and let T be the Fermat (Torricelli) point of triangle ABC. Let A1, B1, and C1 be the feet of the perpendiculars from T to the sides BC, AC, and AB, respectively. Let ω be the circle passing through points A1, B1, and C1. Let A2, B2, and C2 be the second points where ω intersects the sides BC, AC, and AB, respectively (different from A1, B1, C1).

Prove that triangle A2B2C2 is equilateral.

0 replies
Mimii08
3 hours ago
0 replies
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Problem 3 IMO 2005 (Day 1)
Valentin Vornicu   121
N 4 hours ago by Rayvhs
Let $x,y,z$ be three positive reals such that $xyz\geq 1$. Prove that
\[ \frac { x^5-x^2 }{x^5+y^2+z^2} + \frac {y^5-y^2}{x^2+y^5+z^2} + \frac {z^5-z^2}{x^2+y^2+z^5} \geq 0 . \]
Hojoo Lee, Korea
121 replies
Valentin Vornicu
Jul 13, 2005
Rayvhs
4 hours ago
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2024 Putnam A1
KevinYang2.71   21
N 4 hours ago by KAME06
Determine all positive integers $n$ for which there exists positive integers $a$, $b$, and $c$ satisfying
\[ 2a^n+3b^n=4c^n. \]
21 replies
KevinYang2.71
Dec 10, 2024
KAME06
4 hours ago
J
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geo problem saved from graveyard
CrazyInMath   1
N 4 hours ago by Curious_Droid
Source: 3rd KYAC Math-A P5
Given triangle $ABC$ and orthocenter $H$. The foot from $H$ to $BC, CA, AB$ is $D, E, F$ respectively. A point $L$ satisfies that $\odot(LBA)$ and $\odot(LCA)$ are both tangent to $BC$. A circle passing through $B, E$ and tangent to $\odot(BHC)$ intesects $BC$ at another point $P$. $X$ is an arbitrary point on $\odot(PDE)$, and $Y$ is the second intesection point of $\odot(BXE)$ and $\odot(CXD)$.
Prove that $H, Y, L, C$ are concyclic.

Proposed by CrazyInMath.
1 reply
CrazyInMath
Feb 8, 2025
Curious_Droid
4 hours ago
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From a well-known prob
m4thbl3nd3r   3
N 4 hours ago by aaravdodhia
Find all primes $p$ so that $$\frac{7^{p-1}-1}{p}$$can be a perfect square
3 replies
m4thbl3nd3r
Oct 10, 2024
aaravdodhia
4 hours ago
J
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Miklos Schweitzer 1968_9
ehsan2004   1
N Yesterday at 7:52 PM by pi_quadrat_sechstel
Let $ f(x)$ be a real function such that
\[ \lim_{x \rightarrow +\infty} \frac{f(x)}{e^x}=1\]
and $ |f''(x)|\leq c|f'(x)|$ for all sufficiently large $ x$. Prove that \[ \lim_{x \rightarrow +\infty} \frac{f'(x)}{e^x}=1.\]

P. Erdos
1 reply
ehsan2004
Oct 8, 2008
pi_quadrat_sechstel
Yesterday at 7:52 PM
J
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Putnam 1956 B7
sqrtX   7
N Yesterday at 7:08 PM by bjump
Source: Putnam 1956
The polynomials $P(z)$ and $Q(z)$ with complex coefficients have the same set of numbers for their zeros but possibly different multiplicities. The same is true for the polynomials
$$P(z)+1 \;\; \text{and} \;\; Q(z)+1.$$Prove that $P(z)=Q(z).$
7 replies
sqrtX
Jul 5, 2022
bjump
Yesterday at 7:08 PM
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Infinite sum
Thanhdoan1   0
Apr 24, 2025
Calculate the sum
τ(1):1-τ(2):2+τ(3):3-....+(-1)^(n-1)*τ(n):n, with τ(n) is the number of divisors of n.
0 replies
Thanhdoan1
Apr 24, 2025
0 replies
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Infinite sum
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10 posts
Thanhdoan1
#1 h  Apr 24, 2025, 3:26 PM • 1 Y
Y by Exponent11
Calculate the sum
τ(1):1-τ(2):2+τ(3):3-....+(-1)^(n-1)*τ(n):n, with τ(n) is the number of divisors of n.
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