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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.

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[*]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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Worst Sillies of All Time
pingpongmerrily   75
N 3 minutes ago by Aaronjudgeisgoat
Share the worst sillies you have ever made!

Mine was probably on the 2024 MathCounts State Target Round Problem 8, where I wrote my answer as a fraction instead of a percent, which cost me a trip to Nationals that year.
75 replies
pingpongmerrily
May 30, 2025
Aaronjudgeisgoat
3 minutes ago
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S(ai)=S(aj)=S(sigma ai) = n
ilovemath0402   0
11 minutes ago
Source: Inspired by Romania 1999
Given positive integer $m$. Find all $n$ such that there exist non-negative integer $a_1,a_2,\ldots a_m$ satisfied
$$S(a_1)=S(a_2)=\ldots = S(a_m)=S(a_1+a_2+\ldots + a_m) = n$$P/s: original problem
0 replies
ilovemath0402
11 minutes ago
0 replies
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Trivial Factoring MathCounts Question? 2025 MathCounts National Sprint Round #29
ilikemath247365   39
N 12 minutes ago by pingpongmerrily
What is the value of the expression below?

$\frac{(1! + 2! + 3!)(2! + 3! + 4!)(3! + 4! + 5!)...(98! + 99! + 100!)}{(1! - 3(2!) + 3!)(2! - 3(3!) + 4!)(3! - 3(4!) + 5!)...(98! - 3(99!) + 100!)}$.
39 replies
ilikemath247365
May 28, 2025
pingpongmerrily
12 minutes ago
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Trouble focusing
GallopingUnicorn45   1
N 14 minutes ago by Totoro2014
Hi all,

So I'm currently hard-grinding for AIME in AMC 10 this year (I'm taking both A and B) and I'm having a hard time focusing and my productivity is slipping; I can't finish all of the stuff I plan daily and weekly. Before, during the school year, I was also grinding and listening to K-pop while working, and now I have songs stuck in my head as I work, which also makes me unable to focus.

Any tips on how to concentrate for longer periods of time? Thanks!
1 reply
GallopingUnicorn45
32 minutes ago
Totoro2014
14 minutes ago
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S(an) greater than S(n)
ilovemath0402   0
14 minutes ago
Source: Inspired by an old result
Find all positive integer $n$ such that $S(an)\ge S(n) \quad \forall a \in \mathbb{Z}^{+}$ ($S(n)$ is sum of digit of $n$ in base 10)
P/s: Original problem
0 replies
ilovemath0402
14 minutes ago
0 replies
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Parallel lines on a rhombus
buratinogigle   0
20 minutes ago
Source: Own, Entrance Exam for Grade 10 Admission, HSGS 2025
Given the rhombus $ABCD$ with its incircle $\omega$. Let $E$ and $F$ be the points of tangency of $\omega$ with $AB$ and $AC$ respectively. On the edges $CB$ and $CD$, take points $G$ and $H$ such that $GH$ is tangent to $\omega$ at $P$. Suppose $Q$ is the intersection point of the lines $EG$ and $FH$. Prove that two lines $AP$ and $CQ$ are parallel or coincide.
0 replies
buratinogigle
20 minutes ago
0 replies
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Line bisects a segment
buratinogigle   0
29 minutes ago
Source: Own, Entrance Exam for Grade 10 Admission, HSGS 2025
Let $ABC$ be a triangle with $AB = AC$. A circle $(O)$ is tangent to sides $AC$ and $AB$, and $O$ is the midpoint of $BC$. Points $E$ and $F$ lie on sides $AC$ and $AB$, respectively, such that segment $EF$ is tangent to circle $(O)$ at point $P$. Let $H$ and $K$ be the orthocenters of triangles $OBF$ and $OCE$, respectively. Prove that line $OP$ bisects segment $HK$.
0 replies
buratinogigle
29 minutes ago
0 replies
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A prime graph
Eyed   44
N 37 minutes ago by ezpotd
Source: ISL N2
For each prime $p$, construct a graph $G_p$ on $\{1,2,\ldots p\}$, where $m\neq n$ are adjacent if and only if $p$ divides $(m^{2} + 1-n)(n^{2} + 1-m)$. Prove that $G_p$ is disconnected for infinitely many $p$
44 replies
Eyed
Jul 20, 2021
ezpotd
37 minutes ago
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2500th Post!
PikaPika999   27
N 40 minutes ago by PikaPika999
I may be a bit late for this, but this is my 2500th post :)
Also this is going to be my last one until another big milestone bc I don't wanna clog up the MSM forum with my milestones

Also, since my 1000th post math story was locked due to a flamewar, here is my math story with a few updates :)
(This was also scripted so if there are any problems in my story, um... well, it is what it is)

Script starts:


When I had less than 25 posts on AoPS, I saw many people create threads about them getting 1000th posts and their math story. I thought I would never hit 1000 posts, but I did, and that thread got locked...Please


So, lol here we are, writing my math story again :)


Daycare

Preschool

Kindergarten

First Grade

Second Grade

Third Grade

Fourth Grade

Fifth Grade

Sixth Grade

In conclusion, AoPS has helped me improve my math. Minor side note, but

Finally, I would like to say thank you to all the new friends I made and all the instructors on AoPS that taught me!

Another minor side note, but

and here are some problems ig :)

Problems

hopefully these problems weren't too easy lol
27 replies
PikaPika999
May 29, 2025
PikaPika999
40 minutes ago
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Problem 12
SlovEcience   1
N an hour ago by Mathzeus1024
Find all functions \( f: \mathbb{N} \to \mathbb{N} \) such that
\[ f(x^4 + 5y^4 + 10z^4) = f(x)^4 + 5f(y)^4 + 10f(z)^4 \]for all \( x, y, z \in \mathbb{N} \).
1 reply
SlovEcience
Today at 3:46 AM
Mathzeus1024
an hour ago
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Dophantine equation
MENELAUSS   3
N an hour ago by ilikemath247365
Solve for $x;y \in \mathbb{Z}$ the following equation :
$$3^x-8^y =2xy+1 $$
3 replies
MENELAUSS
May 27, 2025
ilikemath247365
an hour ago
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Everyone, please help me with this exercise. Thank you!
bathoi   0
an hour ago
Consider the real sequence (a_n) satisfying the condition
|a_(m+n) - a_m -a_n| <= 1, m & n in N
a. Prove that the sequence (a_n) has a finite limit.
b. Prove that the sequence (a_n) converges.

0 replies
bathoi
an hour ago
0 replies
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A weird problem
jayme   1
N an hour ago by jayme
Dear Mathlinkers,

1. ABC a triangle
2. 0 the circumcircle
3. I the incenter
4. 1 a circle passing througn B and C
5. X, Y the second points of intersection of 1 wrt BI, CI
6. 2 the circumcircle of the triangle XYI
7. M, N the symetrics of B, C wrt XY.

Question : if 2 is tangent to 0 then, 2 is tangent to MN.

Sincerely
Jean-Louis
1 reply
jayme
Today at 6:52 AM
jayme
an hour ago
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Three collinear points
buratinogigle   1
N an hour ago by Giabach298
Source: Own, Entrance Exam for Grade 10 Admission, HSGS 2025
Let $ABC$ be a triangle with points $E$ and $F$ lying on rays $AC$ and $AB$, respectively, such that $AE = AF$. On the line $EF$, choose points $M$ and $N$ such that $CM \perp CA$ and $BN \perp BA$. Let $K$ and $L$ be the feet of the perpendiculars from $M$ and $N$ to line $BC$, respectively. Let $J$ be the intersection point of lines $LF$ and $KE$. Prove that the reflection of $J$ over line $EF$ lies on the line connecting $A$ and the circumcenter of triangle $ABC$.
1 reply
buratinogigle
an hour ago
Giabach298
an hour ago
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Can someone explain this one
hawa   10
N Apr 29, 2025 by VivaanKam
Suppose n is the largest integer obtained by solving the following inequality:

3+9+18+30+...+n
n < 2021.
10 replies
hawa
Apr 29, 2025
VivaanKam
Apr 29, 2025
J
Can someone explain this one
G H J
Reveal topic tags
inequalities
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G H BBookmark kLocked kLocked NReply
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hawa
2 posts
hawa
#1 h  Apr 29, 2025, 1:36 AM
Y by
Suppose n is the largest integer obtained by solving the following inequality:

3+9+18+30+...+n
n < 2021.
Z K Y
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FredyCrooger
64 posts
FredyCrooger
#2 h  Apr 29, 2025, 1:45 AM
Y by
So first you find the change in the difference between the numbers and assuming the question is asking to find the largest $n$, you can add them up and continue from there.
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johnnie.walker
2 posts
johnnie.walker
#3 h  Apr 29, 2025, 1:38 PM
Y by
Hint
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fossasor
611 posts
fossasor
#4 h  Apr 29, 2025, 1:48 PM
Y by
Hint #2
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snake2020
4510 posts
snake2020
#5 h  Apr 29, 2025, 1:51 PM
Y by
Hint #3
This post has been edited 1 time. Last edited by snake2020, Apr 29, 2025, 1:51 PM
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snake2020
4510 posts
snake2020
#6 h  Apr 29, 2025, 2:08 PM
Y by
Solution
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Andrew2019
2329 posts
Andrew2019
#7 h  Apr 29, 2025, 5:32 PM
Y by
snake2020 wrote:
Solution

believe this is incorrect, it says $n$ is less that $2021$, not the sum
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VivaanKam
182 posts
VivaanKam
#8 h  Apr 29, 2025, 8:01 PM
Y by
The general term of the sequence is $a_n=\dfrac{3n(n-1))}{2}$
This post has been edited 1 time. Last edited by VivaanKam, Apr 29, 2025, 8:10 PM
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VivaanKam
182 posts
VivaanKam
#9 h  Apr 29, 2025, 8:04 PM
Y by
But I don't get the problem. Are you saying that $3+9+18+30+\dots +n<2021$ and $n<2021$?
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VivaanKam
182 posts
VivaanKam
#10 h  Apr 29, 2025, 8:05 PM
Y by
nvm I figured it out.
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VivaanKam
182 posts
VivaanKam
#11 h  Apr 29, 2025, 8:23 PM
Y by
Solution
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