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k a April Highlights and 2025 AoPS Online Class Information
jlacosta   0
Apr 2, 2025
Spring is in full swing and summer is right around the corner, what are your plans? At AoPS Online our schedule has new classes starting now through July, so be sure to keep your skills sharp and be prepared for the Fall school year! Check out the schedule of upcoming classes below.

WOOT early bird pricing is in effect, don’t miss out! If you took MathWOOT Level 2 last year, no worries, it is all new problems this year! Our Worldwide Online Olympiad Training program is for high school level competitors. AoPS designed these courses to help our top students get the deep focus they need to succeed in their specific competition goals. Check out the details at this link for all our WOOT programs in math, computer science, chemistry, and physics.

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April 9th (Webinar), 4:00pm PT/7:00pm ET, Learn about Video-based Summer Camps at the Virtual Campus
[*]April 10th (Math Jam), 4:30pm PT/7:30pm ET, 2025 MathILy and MathILy-Er Math Jam: Multibackwards Numbers
[*]April 22nd (Webinar), 4:00pm PT/7:00pm ET, Competitive Programming at AoPS (USACO).[/list]
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0 replies
jlacosta
Apr 2, 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
J
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Hard number theory
truongngochieu   0
7 minutes ago
Find all integers $a,b$ such that $a^2+a+1=7^b$
0 replies
truongngochieu
7 minutes ago
0 replies
J
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GCD of sums of consecutive divisors
Lukaluce   1
N 9 minutes ago by Marius_Avion_De_Vanatoare
Source: EGMO 2025 P1
For a positive integer $N$, let $c_1 < c_2 < ... < c_m$ be all the positive integers smaller than $N$ that are coprime to $N$. Find all $N \ge 3$ such that
\[gcd(N, c_i + c_{i + 1}) \neq 1\]for all $1 \le i \le m - 1$.
1 reply
+4 w
Lukaluce
20 minutes ago
Marius_Avion_De_Vanatoare
9 minutes ago
J
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Arithmetic means as terms of a sequence
Lukaluce   0
19 minutes ago
Source: EGMO 2025 P2
An infinite increasing sequence $a_1 < a_2 < a_3 < ...$ of positive integers is called central if for every positive integer $n$, the arithmetic mean of the first $a_n$ terms of the sequence is equal to $a_n$. Show that there exists an infinite sequence $b_1, b_2, b_3, ...$ of positive integers such that for every central sequence $a_1, a_2, a_3, ...$, there are infinitely many positive integers $n$ with $a_n = b_n$.
0 replies
Lukaluce
19 minutes ago
0 replies
J
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pairwise coprime sum gcd
InterLoop   1
N 24 minutes ago by MaxSze
Source: EGMO 2025/1
For a positive integer $N$, let $c_1 < c_2 < \dots < c_m$ be all the positive integers smaller than $N$ that are coprime to $N$. Find all $N \ge 3$ such that
$$\gcd(N, c_i + c_{i+1}) \neq 1$$for all $1 \le i \le m - 1$.
1 reply
InterLoop
an hour ago
MaxSze
24 minutes ago
J
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postaffteff
JetFire008   18
N 26 minutes ago by Captainscrubz
Source: Internet
Let $P$ be the Fermat point of a $\triangle ABC$. Prove that the Euler line of the triangles $PAB$, $PBC$, $PCA$ are concurrent and the point of concurrence is $G$, the centroid of $\triangle ABC$.
18 replies
1 viewing
JetFire008
Mar 15, 2025
Captainscrubz
26 minutes ago
J
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Similarity
AHZOLFAGHARI   17
N 34 minutes ago by ariopro1387
Source: Iran Second Round 2015 - Problem 3 Day 1
Consider a triangle $ABC$ . The points $D,E$ are on sides $AB,AC$ such that $BDEC$ is a cyclic quadrilateral. Let $P$ be the intersection of $BE$ and $CD$. $H$ is a point on $AC$ such that $\angle PHA = 90^{\circ}$. Let $M,N$ be the midpoints of $AP,BC$. Prove that: $ ACD \sim MNH $.
17 replies
AHZOLFAGHARI
May 7, 2015
ariopro1387
34 minutes ago
J
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one cyclic formed by two cyclic
CrazyInMath   0
an hour ago
Source: EGMO 2025/3
Let $ABC$ be an acute triangle. Points $B, D, E$, and $C$ lie on a line in this order and satisfy $BD = DE = EC$. Let $M$ and $N$ be the midpoints of $AD$ and $AE$, respectively. Suppose triangle $ADE$ is acute, and let $H$ be its orthocentre. Points $P$ and $Q$ lie on lines $BM$ and $CN$, respectively, such that $D, H, M,$ and $P$ are concyclic and pairwise different, and $E, H, N,$ and $Q$ are concyclic and pairwise different. Prove that $P, Q, N,$ and $M$ are concyclic.
0 replies
+12 w
CrazyInMath
an hour ago
0 replies
J
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A problem with non-negative a,b,c
KhuongTrang   3
N an hour ago by KhuongTrang
Source: own
Problem. Let $a,b,c$ be non-negative real variables with $ab+bc+ca\neq 0.$ Prove that$$\color{blue}{\sqrt{\frac{8a^{2}+\left(b-c\right)^{2}}{\left(b+c\right)^{2}}}+\sqrt{\frac{8b^{2}+\left(c-a\right)^{2}}{\left(c+a\right)^{2}}}+\sqrt{\frac{8c^{2}+\left(a-b\right)^{2}}{\left(a+b\right)^{2}}}\ge \sqrt{\frac{18(a^{2}+b^{2}+c^{2})}{ab+bc+ca}}.}$$Equality holds iff $(a,b,c)\sim(t,t,t)$ or $(a,b,c)\sim(t,t,0)$ where $t>0.$
3 replies
KhuongTrang
Mar 4, 2025
KhuongTrang
an hour ago
J
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Number Theory Chain!
JetFire008   52
N an hour ago by Anto0110
I will post a question and someone has to answer it. Then they have to post a question and someone else will answer it and so on. We can only post questions related to Number Theory and each problem should be more difficult than the previous. Let's start!

Question 1
52 replies
JetFire008
Apr 7, 2025
Anto0110
an hour ago
J
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Convex quad
MithsApprentice   81
N an hour ago by LeYohan
Source: USAMO 1993
Let $\, ABCD \,$ be a convex quadrilateral such that diagonals $\, AC \,$ and $\, BD \,$ intersect at right angles, and let $\, E \,$ be their intersection. Prove that the reflections of $\, E \,$ across $\, AB, \, BC, \, CD, \, DA \,$ are concyclic.
81 replies
MithsApprentice
Oct 27, 2005
LeYohan
an hour ago
J
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SMT online indvidual tests
techb   4
N an hour ago by techb
Hi, are you all able to see both of the individual subject tests on your comp.mt for SMT? I can't see mine as I have registered for algebra and calculus, but I only see algebra. (See attachment)

Please respond fast.
4 replies
techb
2 hours ago
techb
an hour ago
J
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Bashtastic
nosysnow   58
N 2 hours ago by AshAuktober
Source: 2018 AIME 1 #11
Find the least positive integer $n$ such that when $3^n$ is written in base $143$, its two right-most digits in base $143$ are $01$.
58 replies
nosysnow
Mar 7, 2018
AshAuktober
2 hours ago
J
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PROM^2 for Girls 2025
mathisfun17   25
N Today at 7:05 AM by Yiyj1
Hi everyone!

The Princeton International School of Math and Science (PRISMS) Math Team is delighted that $PROM^2$ for Girls, PRISMS Online Math Meet for Girls, is happening this spring! https://www.prismsus.org/events/prom/home/index

We warmly invite all middle school girls to join us! This is a fantastic opportunity for young girls to connect with others interested in math as well as prepare for future math contests.

This contest will take place online from 12:00 pm to 3:00 pm EST on Saturday, April 26th, 2025.

The competition will include a team and individual round as well as activities like origami. You can see a detailed schedule here. https://prismsus.org/events/prom/experience/schedule.

Registration is FREE, there are cash prizes for participants who place in the top 10 and cool gifts for all participants.

1st place individual: $500 cash
2nd place individual: $300 cash
3rd place individual: $100 cash
4th-10th place individual: $50 cash each

Some FAQs:
Q: How difficult are the questions?
A: The problem difficulty is around AMC 8 or Mathcounts level.

Q: Are there any example problems?
A: You can find some archived here: https://www.prismsus.org/events/prom/achieve/achieve

Registration is open now. https://www.prismsus.org/events/prom/register/register. Email us at prom2@prismsus.org with any questions.

The PRISMS Peregrines Math Team welcomes you!
25 replies
mathisfun17
Feb 22, 2025
Yiyj1
Today at 7:05 AM
J
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centslordm
centslordm   56
N Today at 4:51 AM by ab456
Source: AIME II #8
From an unlimited supply of 1-cent coins, 10-cent coins, and 25-cent coins, Silas wants to find a collection of coins that has a total value of $N$ cents, where $N$ is a positive integer. He uses the so-called greedy algorithm, successively choosing the coin of greatest value that does not cause the value of his collection to exceed $N.$ For example, to get 42 cents, Silas will choose a 25-cent coin, then a 10-cent coin, then 7 1-cent coins. However, this collection of 9 coins uses more coins than necessary to get a total of 42 cents; indeed, choosing 4 10-cent coins and 2 1-cent coins achieves the same total value with only 6 coins. In general, the greedy algorithm succeeds for a given $N$ if no other collection of 1-cent, 10-cent, and 25-cent coins gives a total value of $N$ cents using strictly fewer coins than the collection given by the greedy algorithm. Find the number of values of $N$ between $1$ and $1000$ inclusive for which the greedy algorithm succeeds.
56 replies
centslordm
Feb 13, 2025
ab456
Today at 4:51 AM
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Pascal, Cayley and Fermat 2025
melpomene7   50
N Mar 29, 2025 by Cerberusman
Anyone else do a CEMC contest? I did fermat but totally fumbled and got a 108.
50 replies
melpomene7
Feb 28, 2025
Cerberusman
Mar 29, 2025
J
Pascal, Cayley and Fermat 2025
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