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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 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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Preparing for Putnam level entrance examinations
Cats_on_a_computer   1
N 13 minutes ago by Miquel-point
Non American high schooler in the equivalent of grade 12 here. Where I live, two the best undergraduates program in the country accepts students based on a common entrance exam. The first half of the exam is “screening”, with 4 options being presented per question, each of which one has to assign a True or False. This first half is about the difficulty of an average AIME, or JEE Adv paper, and it is a requirement for any candidate to achieve at least 24/40 on this half for the examiners to even consider grading the second part. The second part consists of long form questions, and I have, no joke, seen them literally rip off, verbatim, Putnam A6s. Some of the problems are generally standard textbook problems in certain undergrad courses but obviously that doesn’t translate it to being doable for high school students. I’ve effectively got to prepare for a slightly nerfed Putnam, if you will, and so I’ve been looking for resources (not just problems) for Putnam level questions. Does anyone have any suggestions?
1 reply
Cats_on_a_computer
27 minutes ago
Miquel-point
13 minutes ago
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Interesting functional equation with geometry
User21837561   1
N 31 minutes ago by User21837561
Source: BMOSL 2025 G7
For an acute triangle $ABC$, let $O$ be the circumcentre, $H$ be the orthocentre, and $G$ be the centroid.
Let $f:\pi\rightarrow\mathbb R$ satisfy the following condition:
$f(A)+f(B)+f(C)=f(O)+f(G)+f(H)$
Prove that $f$ is constant.
1 reply
User21837561
an hour ago
User21837561
31 minutes ago
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Tangent circles
Sadigly   0
an hour ago
Source: Azerbaijan Junior MO 2025 P6
Let $T$ be a point outside circle $\omega$ centered at $O$. Tangents from $T$ to $\omega$ touch $\omega$ at $A;B$. Line $TO$ intersects bigger $AB$ arc at $C$.The line drawn from $T$ parallel to $AC$ intersects $CB$ at $E$. Ray $TE$ intersects small $BC$ arc at $F$. Prove that the circumcircle of $OEF$ is tangent to $\omega$.
0 replies
1 viewing
Sadigly
an hour ago
0 replies
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Functional Inequality Implies Uniform Sign
peace09   32
N an hour ago by lelouchvigeo
Source: 2023 ISL A2
Let $\mathbb{R}$ be the set of real numbers. Let $f:\mathbb{R}\rightarrow\mathbb{R}$ be a function such that \[f(x+y)f(x-y)\geqslant f(x)^2-f(y)^2\]for every $x,y\in\mathbb{R}$. Assume that the inequality is strict for some $x_0,y_0\in\mathbb{R}$.

Prove that either $f(x)\geqslant 0$ for every $x\in\mathbb{R}$ or $f(x)\leqslant 0$ for every $x\in\mathbb{R}$.
32 replies
1 viewing
peace09
Jul 17, 2024
lelouchvigeo
an hour ago
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Calculating sum of the numbers
Sadigly   0
an hour ago
Source: Azerbaijan Junior MO 2025 P4
A $3\times3$ square is filled with numbers $1;2;3...;9$.The numbers inside four $2\times2$ squares is calculated,and arranged in an increasing order. Is it possible to obtain the following sequences as a result of this operation?

$\text{a)}$ $24,24,25,25$

$\text{b)}$ $20,23,26,29$
0 replies
Sadigly
an hour ago
0 replies
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JBMO type Combinatorics
Sadigly   0
an hour ago
Source: Azerbaijan Junior MO 2025 P3
Alice and Bob take turns taking balloons from a box containing infinitely many balloons. In the first turn, Alice takes $k_1$ amount of balloons, where $\gcd(30;k_1)\neq1$. Then, on his first turn, Bob takes $k_2$ amount of ballons where $k_1<k_2<2k_1$. After first turn, Alice and Bob alternately takes as many balloons as his/her partner has. Is it possible for Bob to take $k_2$ amount of balloons at first, such that after a finite amount of turns, one of them have a number of balloons that is a multiple of $2025^{2025}$?
0 replies
Sadigly
an hour ago
0 replies
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(2^{4n+2}+1)/65 (i) integer, (ii) prime
parmenides51   5
N an hour ago by MR.1
Source: JBMO 2016 Shortlist N3
Find all positive integers $n$ such that the number $A_n =\frac{ 2^{4n+2}+1}{65}$ is
a) an integer,
b) a prime.
5 replies
parmenides51
Oct 14, 2017
MR.1
an hour ago
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Divisibility..
Sadigly   0
an hour ago
Source: Azerbaijan Junior MO 2025 P2
Find all $4$ consecutive even numbers, such that the square of their product is divisible by the sum of their squares.
0 replies
Sadigly
an hour ago
0 replies
J
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This question just asks if you can factorise 12 factorial or not
Sadigly   0
an hour ago
Source: Azerbaijan Junior MO 2025 P1
A teacher creates a fraction using numbers from $1$ to $12$ (including $12$). He writes some of the numbers on the numerator, and writes $\times$ (product) between each number. Then he writes the rest of the numbers in the denominator and also writes $\times$ between each number. There is at least one number both in numerator and denominator. The teacher ensures that the fraction is equal to the smallest possible integer possible.

What is this positive integer, which is also the value of the fraction?
0 replies
Sadigly
an hour ago
0 replies
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harmonic quadrilateral
Lukariman   1
N an hour ago by Lukariman
Given quadrilateral ABCD inscribed in a circle with center O. CA:CB= DA:DB are satisfied. M is any point and d is a line parallel to MC. Radial projection M transforms A,B,D onto line d into A',B',D'. Prove that B' is the midpoint of A'D'.
1 reply
Lukariman
2 hours ago
Lukariman
an hour ago
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Factorising and prime numbers...
Sadigly   4
N 2 hours ago by Nuran2010
Source: Azerbaijan Senior MO 2025 P4
Prove that for any $p>2$ prime number, there exists only one positive number $n$ that makes the equation $n^2-np$ a perfect square of a positive integer
4 replies
Sadigly
Yesterday at 4:19 PM
Nuran2010
2 hours ago
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UC Berkeley Integration Bee 2025 Bracket Rounds
Silver08   8
N 2 hours ago by Aiden-1089
Regular Round

Quarterfinals

Semifinals

3rd Place Match

Finals
8 replies
Silver08
Today at 2:26 AM
Aiden-1089
2 hours ago
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f(x+1)-f(x)=f'(x+1/2) implies f(x)=ax^2 +bx+c?
tom-nowy   1
N 3 hours ago by ddot1
Source: https://artofproblemsolving.com/community/c4t157249f4h1288200
Is this true?

$f: \mathbb{R} \to \mathbb{R}$ is differentiable and for all $x \in \mathbb{R}, \; f(x+1)-f(x)=f'\left(x+\frac{1}{2}\right)$
$\Longrightarrow f(x)=ax^2 +bx+c$.
1 reply
tom-nowy
Today at 2:47 AM
ddot1
3 hours ago
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Integration Bee Kaizo
Calcul8er   57
N Today at 2:00 AM by Silver08
Hey integration fans. I decided to collate some of my favourite and most evil integrals I've written into one big integration bee problem set. I've been entering integration bees since 2017 and I've been really getting hands on with the writing side of things over the last couple of years. I hope you'll enjoy!
57 replies
Calcul8er
Mar 2, 2025
Silver08
Today at 2:00 AM
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Polynomial Limit
P162008   1
N Apr 29, 2025 by P162008
Let $p = \lim_{y\to\infty} \left(\frac{2}{y^2} \left(\lim_{z\to\infty} \frac{1}{z^4} \left(\lim_{x\to 0} \frac{((y^2 + y + 1)x^k + 1)^{z^2 + z + 1} - ((z^2 + z + 1)x^k + 1)^{y^2 + y + 1}}{x^{2k}}\right)\right)\right)^y$ where $k \in N$ and $q = \lim_{n\to\infty} \left(\frac{\binom{2n}{n}. n!}{n^n}\right)^{1/n}$ where $n \in N$. Find the value of $p.q.$
1 reply
P162008
Apr 25, 2025
P162008
Apr 29, 2025
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Polynomial Limit
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P162008
186 posts
P162008
#1 h  Apr 25, 2025, 1:47 AM
Y by
Let $p = \lim_{y\to\infty} \left(\frac{2}{y^2} \left(\lim_{z\to\infty} \frac{1}{z^4} \left(\lim_{x\to 0} \frac{((y^2 + y + 1)x^k + 1)^{z^2 + z + 1} - ((z^2 + z + 1)x^k + 1)^{y^2 + y + 1}}{x^{2k}}\right)\right)\right)^y$ where $k \in N$ and $q = \lim_{n\to\infty} \left(\frac{\binom{2n}{n}. n!}{n^n}\right)^{1/n}$ where $n \in N$. Find the value of $p.q.$
This post has been edited 2 times. Last edited by P162008, Apr 28, 2025, 6:32 AM
Reason: Typo
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P162008
186 posts
P162008
#2 h  Apr 29, 2025, 4:05 AM
Y by
Solution
This post has been edited 17 times. Last edited by P162008, Apr 29, 2025, 5:15 AM
Reason: Typo
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