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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)!

Be sure to mark your calendars for the following upcoming events:
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[*]May 19th, 4:30pm PT/7:30pm ET, What's Next After Beast Academy?, designed for students finishing Beast Academy and ready for Prealgebra 1.
[*]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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Diophantine involving cube
Sadigly   2
N 19 minutes ago by Adywastaken
Source: Azerbaijan Senior NMO 2020
$a;b;c;d\in\mathbb{Z^+}$. Solve the equation: $$2^{a!}+2^{b!}+2^{c!}=d^3$$
2 replies
Sadigly
Yesterday at 10:13 PM
Adywastaken
19 minutes ago
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Nice R+ FE
math_comb01   4
N 20 minutes ago by mkultra42
Source: XOOK 2025 P3
Find all functions $f : \mathbb{R}_{>0} \to \mathbb{R}_{>0}$ so that for any $x, y \in \mathbb{R}_{>0}$, we have \[ f(xf(x^2)+yf(x))=xf(y+xf(x)). \]
Proposed by Anmol Tiwari and MathLuis
4 replies
math_comb01
Feb 9, 2025
mkultra42
20 minutes ago
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2018 JBMO TST- Macedonia, problem 4
Lukaluce   4
N 30 minutes ago by Erto2011_
Source: 2018 JBMO TST- Macedonia
Determine all pairs $(p, q)$, $p, q \in \mathbb {N}$, such that

$(p + 1)^{p - 1} + (p - 1)^{p + 1} = q^q$.
4 replies
Lukaluce
May 28, 2019
Erto2011_
30 minutes ago
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solve in positive integers: 3 \cdot 2^x +4 =n^2
parmenides51   4
N an hour ago by AylyGayypow009
Source: Greece JBMO TST 2019 p2
Find all pairs of positive integers $(x,n) $ that are solutions of the equation $3 \cdot 2^x +4 =n^2$.
4 replies
parmenides51
Apr 29, 2019
AylyGayypow009
an hour ago
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ISI UGB 2025 P7
SomeonecoolLovesMaths   10
N an hour ago by Mathworld314
Source: ISI UGB 2025 P7
Consider a ball that moves inside an acute-angled triangle along a straight line, unit it hits the boundary, which is when it changes direction according to the mirror law, just like a ray of light (angle of incidence = angle of reflection). Prove that there exists a triangular periodic path for the ball, as pictured below.

IMAGE
10 replies
1 viewing
SomeonecoolLovesMaths
Yesterday at 11:28 AM
Mathworld314
an hour ago
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Trigo relation in a right angled. ISIBS2011P10
Sayan   12
N an hour ago by SomeonecoolLovesMaths
Show that the triangle whose angles satisfy the equality
\[\frac{\sin^2A+\sin^2B+\sin^2C}{\cos^2A+\cos^2B+\cos^2C} = 2\]
is right angled.
12 replies
Sayan
Mar 31, 2013
SomeonecoolLovesMaths
an hour ago
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Six variables
Nguyenhuyen_AG   4
N an hour ago by Sunjee
Let $a,\,b,\,c,\,x,\,y,\,z$ be six positive real numbers. Prove that
$$\frac{a}{b+c} \cdot \frac{y+z}{x} + \frac{b}{c+a} \cdot \frac{z+x}{y} + \frac{c}{a+b} \cdot \frac{x+y}{z} \geqslant 2+\sqrt{\frac{8abc}{(a+b)(b+c)(c+a)}}.$$
4 replies
Nguyenhuyen_AG
Yesterday at 5:09 AM
Sunjee
an hour ago
J
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Expressing polynomial as product of two polynomials
Sadigly   3
N 2 hours ago by Sadigly
Source: Azerbaijan Senior NMO 2021
Define $P(x)=((x-a_1)(x-a_2)...(x-a_n))^2 +1$, where $a_1,a_2...,a_n\in\mathbb{Z}$ and $n\in\mathbb{N^+}$. Prove that $P(x)$ couldn't be expressed as product of two non-constant polynomials with integer coefficients.
3 replies
Sadigly
Yesterday at 9:10 PM
Sadigly
2 hours ago
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Product of consecutive terms divisible by a prime number
BR1F1SZ   2
N 2 hours ago by bin_sherlo
Source: 2025 Francophone MO Seniors P4
Determine all sequences of strictly positive integers $a_1, a_2, a_3, \ldots$ satisfying the following two conditions:
[list]
[*]There exists an integer $M > 0$ such that, for all indices $n \geqslant 1$, $0 < a_n \leqslant M$.
[*]For any prime number $p$ and for any index $n \geqslant 1$, the number
\[ a_n a_{n+1} \cdots a_{n+p-1} - a_{n+p} \]is a multiple of $p$.
[/list]


2 replies
BR1F1SZ
Yesterday at 12:09 AM
bin_sherlo
2 hours ago
J
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Pentagon with given diameter, ratio desired
bin_sherlo   2
N 2 hours ago by Umudlu
Source: Türkiye 2025 JBMO TST P7
$ABCDE$ is a pentagon whose vertices lie on circle $\omega$ where $\angle DAB=90^{\circ}$. Let $EB$ and $AC$ intersect at $F$, $EC$ meet $BD$ at $G$. $M$ is the midpoint of arc $AB$ on $\omega$, not containing $C$. If $FG\parallel DE\parallel CM$ holds, then what is the value of $\frac{|GE|}{|GD|}$?
2 replies
bin_sherlo
Yesterday at 7:21 PM
Umudlu
2 hours ago
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dirichlet
spiralman   0
3 hours ago
Let n be a positive integer. Consider 2n+1 distinct positive integers whose total sum is less than (n+1)(3n+1). Prove that among these 2n+1 numbers, there exist two numbers whose sum is 2n+1.
0 replies
spiralman
3 hours ago
0 replies
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Inequalities
sqing   0
4 hours ago
Let $ a, b, c >0, a^2 + \frac{b}{a} = 8 $ and $ 3a + b + c \geq 9\sqrt{3} .$ Prove that $$ ab + c^2\geq 18$$
0 replies
sqing
4 hours ago
0 replies
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Plz help
Bet667   2
N 5 hours ago by jasperE3
f:R-->R for any integer x,y
f(yf(x)+f(xy))=(x+f(x))f(y)
find all function f
(im not good at english)
2 replies
Bet667
Jan 28, 2024
jasperE3
5 hours ago
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Functional equation
TuZo   2
N 5 hours ago by jasperE3
My question is, if we can determinate or not, all $f:R\to R$ continuous function with $sin(f(x+y))=sin(f(x)+f(y))$ for all real $x,y$.
Thank you!
2 replies
TuZo
Oct 23, 2018
jasperE3
5 hours ago
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geometry
carvaan   1
N Apr 20, 2025 by Lankou
The difference between two angles of a triangle is 24°. All angles are numerically double digits. Find the number of possible values of the third angle.
1 reply
carvaan
Apr 20, 2025
Lankou
Apr 20, 2025
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geometry
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Reveal topic tags
geometry
Angle Chasing
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carvaan
3 posts
carvaan
#1 h  Apr 20, 2025, 5:46 PM
Y by
The difference between two angles of a triangle is 24°. All angles are numerically double digits. Find the number of possible values of the third angle.
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Lankou
1399 posts
Lankou
#2 h  Apr 20, 2025, 6:38 PM
Y by
$\alpha-\beta=24$
if $\alpha$ and $\beta$ are double digits $(\alpha, \beta) \in \{(34, 10), (35, 11)....(99, 75)\}$
$\gamma=180-\alpha-\beta$
Since $\gamma$ is double digits, then the possibilities for $\alpha$ and $\beta$ must be reduced to $\{(53, 29), (54, 30), ....(97, 73)\}$
There are 45 possible values for the third angle
This post has been edited 1 time. Last edited by Lankou, Apr 20, 2025, 6:39 PM
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