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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]
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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
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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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USAJMO problem 2: Side lengths of an acute triangle
BOGTRO   59
N 25 minutes ago by ostriches88
Source: Also USAMO problem 1
Find all integers $n \geq 3$ such that among any $n$ positive real numbers $a_1, a_2, \hdots, a_n$ with $\text{max}(a_1,a_2,\hdots,a_n) \leq n \cdot \text{min}(a_1,a_2,\hdots,a_n)$, there exist three that are the side lengths of an acute triangle.
59 replies
BOGTRO
Apr 24, 2012
ostriches88
25 minutes ago
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Inspired by Kosovo 2010
sqing   1
N 33 minutes ago by ytChen
Source: Own
Let $ a,b>0 , a+b\leq k $. Prove that
$$\left(1+\frac{1}{a(b+1)}\right)\left(1+\frac{1}{b(a+1)}\right)\geq\left(1+\frac{4}{k(k+2)}\right)^2$$$$\left(1+\frac {a}{b(a+1)}\right)\left(1+\frac {b}{a(b+1)}\right) \geq\left(1+\frac{2}{k+2}\right)^2$$Let $ a,b>0 , a+b\leq 2 $. Prove that
$$\left(1+\frac{1}{a(b+1)}\right)\left(1+\frac{1}{b(a+1)}\right)\geq \frac{9}{4} $$$$\left(1+\frac {a}{b(a+1)}\right)\left(1+\frac {b}{a(b+1)}\right) \geq \frac{9}{4} $$
1 reply
sqing
Today at 3:56 AM
ytChen
33 minutes ago
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how can I solve this FE
Jackson0423   5
N 33 minutes ago by Jackson0423

Let \( f : \mathbb{R} \to \mathbb{R} \) be a function that satisfies the following equation for all real numbers \( x \):
\[ f(x^2 + x + 3) + 2f(x^2 - 3x + 5) = 6x^2 - 10x + 17. \]Find the value of \( f(100) \).
5 replies
Jackson0423
an hour ago
Jackson0423
33 minutes ago
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Number Theory
VicKmath7   5
N 39 minutes ago by Adywastaken
Source: Archimedes Junior 2014
Let $p$ prime and $m$ a positive integer. Determine all pairs $( p,m)$ satisfying the equation: $ p(p+m)+p=(m+1)^3$
5 replies
VicKmath7
Mar 17, 2020
Adywastaken
39 minutes ago
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x+y in B iff x,y in A
fattypiggy123   5
N 43 minutes ago by Math2030
Source: China Mathematical Olympiad 2015 Q3
Let $n \geq 5$ be a positive integer and let $A$ and $B$ be sets of integers satisfying the following conditions:

i) $|A| = n$, $|B| = m$ and $A$ is a subset of $B$
ii) For any distinct $x,y \in B$, $x+y \in B$ iff $x,y \in A$

Determine the minimum value of $m$.
5 replies
fattypiggy123
Dec 20, 2014
Math2030
43 minutes ago
J
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IMO Genre Predictions
ohiorizzler1434   65
N an hour ago by Oksutok
Everybody, with IMO upcoming, what are you predictions for the problem genres?


Personally I predict: predict
65 replies
ohiorizzler1434
May 3, 2025
Oksutok
an hour ago
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k^2/p for k =1 to (p-1)/2
truongphatt2668   1
N an hour ago by Double07
Let $p$ be a prime such that: $p = 4k+1$. Simplify:
$$\sum_{k=1}^{\frac{p-1}{2}}\begin{Bmatrix}\dfrac{k^2}{p}\end{Bmatrix}$$
1 reply
truongphatt2668
3 hours ago
Double07
an hour ago
J
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Interesting inequality
imnotgoodatmathsorry   1
N an hour ago by Bergo1305
Let $x,y,z > \frac{1}{2}$ and $x+y+z=3$.Prove that:
$\sqrt{x^3+y^3+3xy-1}+\sqrt{y^3+z^3+3yz-1}+\sqrt{z^3+x^3+3zx-1}+\frac{1}{4}(x+5)(y+5)(z+5) \le 60$
1 reply
1 viewing
imnotgoodatmathsorry
2 hours ago
Bergo1305
an hour ago
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every lucky set of values {a_1,a_2,..,a_n} satisfies a_1+a_2+...+a_n >n2^{n-1}
parmenides51   6
N an hour ago by jonh_malkovich
Source: 2020 International Olympiad of Metropolises P3
Let $n>1$ be a given integer. The Mint issues coins of $n$ different values $a_1, a_2, ..., a_n$, where each $a_i$ is a positive integer (the number of coins of each value is unlimited). A set of values $\{a_1, a_2,..., a_n\}$ is called lucky, if the sum $a_1+ a_2+...+ a_n$ can be collected in a unique way (namely, by taking one coin of each value).
(a) Prove that there exists a lucky set of values $\{a_1, a_2, ..., a_n\}$ with $$a_1+ a_2+...+ a_n < n \cdot 2^n.$$(b) Prove that every lucky set of values $\{a_1, a_2,..., a_n\}$ satisfies $$a_1+ a_2+...+ a_n >n \cdot 2^{n-1}.$$
Proposed by Ilya Bogdanov
6 replies
parmenides51
Dec 19, 2020
jonh_malkovich
an hour ago
J
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A strange NT problem
flower417477   0
an hour ago
Source: unknown
$p$ is a given prime number.$A=\{a_1,a_2,\cdots,a_{p-1}\}$ is a set which $\prod\limits_{i=1}^{p-1}a_i\equiv\frac{p-1}{2}\pmod p$.
Prove that there're at least $\frac{p-1}{2}$ non-empty subsets $B$ of $A$ such that $\sum\limits_{b\in B}b\equiv 1\pmod p$
0 replies
flower417477
an hour ago
0 replies
J
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combi/nt
blug   0
an hour ago
Prove that every positive integer $n$ can be written in the form
$$n=2^{a_1}3^{b_1}+2^{a_2}3^{b_2}+..., $$where $a_i, b_j$ are non negative integers, such that
$$2^x3^y\nmid 2^z3^t$$for every $x, y, z, t$.
0 replies
blug
an hour ago
0 replies
J
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high tech FE as J1?!
imagien_bad   60
N 2 hours ago by SimplisticFormulas
Source: USAJMO 2025/1
Let $\mathbb Z$ be the set of integers, and let $f\colon \mathbb Z \to \mathbb Z$ be a function. Prove that there are infinitely many integers $c$ such that the function $g\colon \mathbb Z \to \mathbb Z$ defined by $g(x) = f(x) + cx$ is not bijective.
Note: A function $g\colon \mathbb Z \to \mathbb Z$ is bijective if for every integer $b$, there exists exactly one integer $a$ such that $g(a) = b$.
60 replies
+1 w
imagien_bad
Mar 20, 2025
SimplisticFormulas
2 hours ago
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k Can I make the IMO team next year?
aopslover08   26
N 5 hours ago by steve4916
Hi everyone,

I am a current 11th grader living in Orange, Texas. I recently started doing competition math and I think I am pretty good at it. Recently I did a mock AMC8 and achieved a score of 21/25, which falls in the top 1% DHR. I also talked to my math teacher and she says I am an above average student.

Given my natural talent and the fact that I am willing to work ~3.5 hours a week studying competition math, do you think I will be able to make IMO next year? I am aware of the difficulty of this task but my mom says that I can achieve whatever I put my mind to, as long as I work hard.

Here is my plan for the next few months:

month 1-2: finish studying pre-algebra and learn geometry
month 3-4: learn pre-calculus
month 5-6: start doing IMO shortlist problems
month 7+: keep doing ISL/IMO problems.

Is this a feasible task? I am a girl btw.
26 replies
aopslover08
Yesterday at 7:46 PM
steve4916
5 hours ago
J
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Isosceles everywhere
reallyasian   28
N 5 hours ago by MATHS_ENTUSIAST
Source: 2020 AIME I #1
In $\triangle ABC$ with $AB=AC$, point $D$ lies strictly between $A$ and $C$ on side $\overline{AC}$, and point $E$ lies strictly between $A$ and $B$ on side $\overline{AB}$ such that $AE=ED=DB=BC$. The degree measure of $\angle ABC$ is $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$.
28 replies
reallyasian
Mar 12, 2020
MATHS_ENTUSIAST
5 hours ago
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I'm trying to find a good math comp...
ysn613   9
N May 6, 2025 by anticodon
Okay, so I'm in sixth grade. I have been doing AMC 8 since fourth grade, but not anything else. I was wondering what other "good" math competitions there are that I am the right age for.

I'm also looking for prep tips for math competitions, because when I (mock)ace 2000-2010 AMC 8 and then get a 19 on the real thing when I was definitely able to solve everything, I feel like what I'm doing isn't really working. Anyone got any ideas? Thanks!
9 replies
ysn613
Apr 30, 2025
anticodon
May 6, 2025
J
I'm trying to find a good math comp...
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Reveal topic tags
AMC 8
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ysn613
112 posts
ysn613
#1 h  Apr 30, 2025, 4:12 PM
Y by
Okay, so I'm in sixth grade. I have been doing AMC 8 since fourth grade, but not anything else. I was wondering what other "good" math competitions there are that I am the right age for.

I'm also looking for prep tips for math competitions, because when I (mock)ace 2000-2010 AMC 8 and then get a 19 on the real thing when I was definitely able to solve everything, I feel like what I'm doing isn't really working. Anyone got any ideas? Thanks!
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Gavin_Deng
812 posts
Gavin_Deng
#2 h  Apr 30, 2025, 4:18 PM
Y by
Mathcounts and AMC 10. If you start grinding now you will make aime by 7th grade.
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martianrunner
201 posts
martianrunner
#3 h  Apr 30, 2025, 5:05 PM
Y by
usually earlier amc8s are easier anyways, so that score gap is normal.

a few competitions for that level:

noetic math competition
mathcounts
amc10 (you should start practicing amc10 level stuff)
kangaroo
mathleague
pimath (by alphastar)
CML

these are all individual by the way, if you are looking for some team competitions then there are a few:

mmt (mustang math tournament)
pcmm (purple comet math meet)
bmmt (berkeley mini math tournament)

these are the main ones that i know of

as a starting point, did you read AOPS' introductory books? they are really helpful when starting out.
This post has been edited 3 times. Last edited by martianrunner, Apr 30, 2025, 5:13 PM
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Konigsberg
2225 posts
Konigsberg
#4 h  May 1, 2025, 6:08 AM
Y by
See the contests listed at A1/A2/B1 Elementary/Junior in this guide: https://tinyurl.com/ContestGuideIntl. However, I only included contests which have past exams published (which I think is a good filter anyway for contest quality).
Z K Y
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Chonkachu
1216 posts
Chonkachu
#5 h  May 1, 2025, 9:29 AM
Y by
is geo and intro to algebra b worth it for amc 10?
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MathPerson12321
3749 posts
MathPerson12321
#9 h  May 1, 2025, 6:08 PM • 1 Y
Y by Chonkachu
Chonkachu wrote:
is geo and intro to algebra b worth it for amc 10?

yes
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ysn613
112 posts
ysn613
#12 h  May 6, 2025, 4:24 PM
Y by
Any practice strats?
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Gavin_Deng
812 posts
Gavin_Deng
#13 h  May 6, 2025, 4:26 PM
Y by
Do problems in the time limit. Then when you run out of time keep doing the problems you didn’t solve. Then read the solutions for the problems you didn’t solve.
ysn613 wrote:
Any practice strats?
Z K Y
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Craftybutterfly
467 posts
Craftybutterfly
#14 h  May 6, 2025, 7:48 PM
Y by
ysn613 wrote:
Any practice strats?

You can ask your sibling or parents to chose a random previous AMC 8 or 10 test and you have to complete it in 45 minutes or 40 minutes.
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anticodon
158 posts
anticodon
#15 h  May 6, 2025, 8:41 PM
Y by
use mathdash or alcumus
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