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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:
[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.
[*]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]
Our full course list for upcoming classes is below:
All classes run 7:30pm-8:45pm ET/4:30pm - 5:45pm PT unless otherwise noted.

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0 replies
jlacosta
May 1, 2025
0 replies
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
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
Stop Projecting your insecurities
naman12   53
N 22 minutes ago by EeEeRUT
Source: 2022 USA TST #2
Let $ABC$ be an acute triangle. Let $M$ be the midpoint of side $BC$, and let $E$ and $F$ be the feet of the altitudes from $B$ and $C$, respectively. Suppose that the common external tangents to the circumcircles of triangles $BME$ and $CMF$ intersect at a point $K$, and that $K$ lies on the circumcircle of $ABC$. Prove that line $AK$ is perpendicular to line $BC$.

Kevin Cong
53 replies
naman12
Dec 12, 2022
EeEeRUT
22 minutes ago
9 How many squares do you have memorized
LXC007   107
N 24 minutes ago by SapphireKitty
How many squares have you memorized. I have 1-20

Edit: to clarify i mean positive squares from 1 so if you say ten you mean you memorized the squares 1,2,3,4,5,6,7,8,9 and 10
107 replies
LXC007
May 17, 2025
SapphireKitty
24 minutes ago
Roots of unity
Henryfamz   1
N 28 minutes ago by Mathzeus1024
Compute $$\sec^4\frac\pi7+\sec^4\frac{2\pi}7+\sec^4\frac{3\pi}7$$
1 reply
Henryfamz
May 13, 2025
Mathzeus1024
28 minutes ago
Shortest number theory you might've seen in your life
AlperenINAN   11
N 28 minutes ago by Assassino9931
Source: Turkey JBMO TST 2025 P4
Let $p$ and $q$ be prime numbers. Prove that if $pq(p+1)(q+1)+1$ is a perfect square, then $pq + 1$ is also a perfect square.
11 replies
AlperenINAN
May 11, 2025
Assassino9931
28 minutes ago
Inspired by qrxz17
sqing   1
N 34 minutes ago by lbh_qys
Source: Own
Let $a, b,c>0 ,(a^2+b^2+c^2)^2 - 2(a^4+b^4+c^4) = 27 $. Prove that $$a+b+c\geq 3\sqrt {3}$$
1 reply
sqing
an hour ago
lbh_qys
34 minutes ago
AZE JBMO TST
IstekOlympiadTeam   10
N 41 minutes ago by Assassino9931
Source: AZE JBMO TST
Prove that there are not intgers $a$ and $b$ with conditions,
i) $16a-9b$ is a prime number.
ii) $ab$ is a perfect square.
iii) $a+b$ is also perfect square.
10 replies
IstekOlympiadTeam
May 2, 2015
Assassino9931
41 minutes ago
Iran TST Starter
M11100111001Y1R   3
N 43 minutes ago by dgrozev
Source: Iran TST 2025 Test 1 Problem 1
Let \( a_n \) be a sequence of positive real numbers such that for every \( n > 2025 \), we have:
\[
a_n = \max_{1 \leq i \leq 2025} a_{n-i} - \min_{1 \leq i \leq 2025} a_{n-i}
\]Prove that there exists a natural number \( M \) such that for all \( n > M \), the following holds:
\[
a_n < \frac{1}{1404}
\]
3 replies
M11100111001Y1R
May 27, 2025
dgrozev
43 minutes ago
An interesting functional equation
giannis2006   3
N 43 minutes ago by GreekIdiot
Source: Own
Find all functions $f:R^+->R^+$ such that:
$f(xf(y))=xy-xf(x)+f(x)^2$ for all $x,y>0$

The most difficult version of this problem is the following:
Find all functions $f:R^+->R^+$ such that:
$f(xf(y+f(x)))=xy+f(x)^2$ for all $x,y>0$
3 replies
giannis2006
Jun 8, 2023
GreekIdiot
43 minutes ago
A long non-classical problem
M11100111001Y1R   1
N an hour ago by dgrozev
Source: Iran TST 2025 Test 3 Problem 2
Suppose \( n \in \mathbb{N} \) is a natural number. A function \( f(x, y) \) is called \textit{\( n \)-friendly} if for fewer than 1\% of the integers \( k \) with \( -n \leq k \leq n \), the equation \( f(x, y) = k \) has a solution in natural numbers \( (x, y) \) such that \( \frac{y_0}{x_0} \in \left[\frac{1}{100}, 100\right] \), where \( (x_0, y_0) \) is a solution. Suppose \( f(x, y) \leq g(x, y) \), where \( g(x, y) \) is a polynomial with real coefficients, negative leading coefficients, and total degree greater than 2, and for every real number \( x \), we have \( g(x, y) \to \infty \) as \( \frac{y}{x} \in \left[\frac{1}{100}, 100\right] \). Prove that for sufficiently large \( n \), the function \( f \) is not \( n \)-friendly.
1 reply
M11100111001Y1R
May 27, 2025
dgrozev
an hour ago
Another FE
M11100111001Y1R   1
N an hour ago by Mathzeus1024
Source: Iran TST 2025 Test 2 Problem 3
Find all functions $f: \mathbb{R}^+ \to \mathbb{R}^+$ such that for all $x,y>0$ we have:
$$f(f(f(xy))+x^2)=f(y)(f(x)-f(x+y))$$
1 reply
M11100111001Y1R
2 hours ago
Mathzeus1024
an hour ago
Problem 9
SlovEcience   0
an hour ago
Let the sequence $(x_n)$ be defined by
\[
x_1 = 2,\quad x_{n+1} = x_n + \frac{n}{x_n},\quad \text{for all } n \geq 1.
\]Prove that the sequences \( y_n = \frac{x_n}{n} \) and \( z_n = x_n - n \) have finite limits, and find those limits.
0 replies
SlovEcience
an hour ago
0 replies
9 Mock AMC 8
Leeoz   2
N 5 hours ago by Yihangzh
This is just your average mock AMC 8 on AoPS... nothing sus at all...
Just PM me your answers if you actually want to try it and be on the leaderboard...

Leaderboard

This test is for entertainment purposes only...

Also if you all want, I can post the solutions in June.
2 replies
Leeoz
5 hours ago
Yihangzh
5 hours ago
Trivial Factoring MathCounts Question? 2025 MathCounts National Sprint Round #29
ilikemath247365   26
N 5 hours ago by Schintalpati
What is the value of the expression below?

$\frac{(1! + 2! + 3!)(2! + 3! + 4!)(3! + 4! + 5!)...(98! + 99! + 100!)}{(1! - 3(2!) + 3!)(2! - 3(3!) + 4!)(3! - 3(4!) + 5!)...(98! - 3(99!) + 100!)}$.
26 replies
ilikemath247365
Yesterday at 1:16 AM
Schintalpati
5 hours ago
Overly wordy problems
ZMB038   4
N Today at 3:31 AM by CJB19
Hey everyone, here we can post questions with way to many extraneous words, that are actually easy.
Try to solve the one above yours.
I'll start:
Click to reveal hidden text
4 replies
ZMB038
Yesterday at 11:14 PM
CJB19
Today at 3:31 AM
Mathcounts Target Resources
sadas123   3
N Mar 29, 2025 by Andyluo
I was wondering what I could use to practice for Mathcount Target rounds because my sprint is normally 23-25+ (Depending on the level: This is for Chapter, but some times for states) but my target is normally 8-10 (Depending on the level: This is normally for states and some time Nats) and I want that to go up to 12-14 So I was wondering what are some good resources to build that problem solving knowledge for target, and some resources that will help me learn the complex problems on there mostly for Geometry and Algebra.
3 replies
sadas123
Mar 29, 2025
Andyluo
Mar 29, 2025
Mathcounts Target Resources
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G H BBookmark kLocked kLocked NReply
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sadas123
1326 posts
#1
Y by
I was wondering what I could use to practice for Mathcount Target rounds because my sprint is normally 23-25+ (Depending on the level: This is for Chapter, but some times for states) but my target is normally 8-10 (Depending on the level: This is normally for states and some time Nats) and I want that to go up to 12-14 So I was wondering what are some good resources to build that problem solving knowledge for target, and some resources that will help me learn the complex problems on there mostly for Geometry and Algebra.
This post has been edited 1 time. Last edited by sadas123, Mar 29, 2025, 8:17 PM
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Inaaya
423 posts
#2
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what level is this?
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sadas123
1326 posts
#3
Y by
Inaaya wrote:
what level is this?

oh.. I just edited this and added it.
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Andyluo
1003 posts
#4
Y by
For MATHCOUNTS target, the main importance is practicing harder tests, and doing harder contests such as the AMC 10/AIME with longer times.

Sprint I've realized that the theory is usually really easy, (but at some level you have to practice it) the main emphasis is not sillying and going insanely fast
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