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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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Minimum of this fuction
persamaankuadrat   1
N 8 minutes ago by alexheinis
Source: KTOM January 2020
If $x$ is a positive real number, find the minimum of the following expression

$$\lfloor x \rfloor + \frac{500}{\lceil x\rceil^{2}}$$
1 reply
persamaankuadrat
an hour ago
alexheinis
8 minutes ago
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Find the remainder
Jackson0423   0
15 minutes ago

Find the remainder when
\[ \frac{5^{2000} - 1}{4} \]is divided by \(64\).
0 replies
1 viewing
Jackson0423
15 minutes ago
0 replies
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A well-known circle hides in the dark
darij grinberg   15
N 44 minutes ago by TUAN2k8
Source: All-Russian Olympiad 2006 finals, problem 11.4 (problem 4 for grade 11)
Given a triangle $ ABC$. The angle bisectors of the angles $ ABC$ and $ BCA$ intersect the sides $ CA$ and $ AB$ at the points $ B_1$ and $ C_1$, and intersect each other at the point $ I$. The line $ B_1C_1$ intersects the circumcircle of triangle $ ABC$ at the points $ M$ and $ N$. Prove that the circumradius of triangle $ MIN$ is twice as long as the circumradius of triangle $ ABC$.
15 replies
darij grinberg
May 6, 2006
TUAN2k8
44 minutes ago
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unsolved nt
MuradSafarli   1
N an hour ago by whwlqkd
Find all prime numbers $p$ such that $p^2 - 12$ is also a prime number.
1 reply
MuradSafarli
an hour ago
whwlqkd
an hour ago
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IMO Problem 4
iandrei   106
N an hour ago by alexanderchew
Source: IMO ShortList 2003, geometry problem 1
Let $ABCD$ be a cyclic quadrilateral. Let $P$, $Q$, $R$ be the feet of the perpendiculars from $D$ to the lines $BC$, $CA$, $AB$, respectively. Show that $PQ=QR$ if and only if the bisectors of $\angle ABC$ and $\angle ADC$ are concurrent with $AC$.
106 replies
iandrei
Jul 14, 2003
alexanderchew
an hour ago
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interesting diophantiic fe in natural numbers
skellyrah   0
an hour ago
Find all functions \( f : \mathbb{N} \to \mathbb{N} \) such that for all \( m, n \in \mathbb{N} \),
\[ mn + f(n!) = f(f(n))! + n \cdot \gcd(f(m), m!). \]
0 replies
skellyrah
an hour ago
0 replies
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Three numbers cannot be squares simultaneously
WakeUp   39
N an hour ago by MR.1
Source: APMO 2011
Let $a,b,c$ be positive integers. Prove that it is impossible to have all of the three numbers $a^2+b+c,b^2+c+a,c^2+a+b$ to be perfect squares.
39 replies
WakeUp
May 18, 2011
MR.1
an hour ago
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FE over R
IAmTheHazard   21
N an hour ago by benjaminchew13
Source: ELMO Shortlist 2024/A3
Find all functions $f : \mathbb{R}\to\mathbb{R}$ such that for all real numbers $x$ and $y$,
$$f(x+f(y))+xy=f(x)f(y)+f(x)+y.$$
Andrew Carratu
21 replies
IAmTheHazard
Jun 22, 2024
benjaminchew13
an hour ago
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Nice one
Blacklord   10
N 2 hours ago by Pal702004
Source: ....
Find all integers numbers (a,b,c) such that
$a/b + b/c + c/a =3$
10 replies
Blacklord
Jan 26, 2017
Pal702004
2 hours ago
J
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Four points are concyclic
DreamTeam   9
N 2 hours ago by AylyGayypow009
Source: Moldova IMO-BMO TST 2003, day 1, problem 3
Let $ ABCD$ be a quadrilateral inscribed in a circle of center $ O$. Let M and N be the midpoints of diagonals $ AC$ and $ BD$, respectively and let $ P$ be the intersection point of the diagonals $ AC$ and $ BD$ of the given quadrilateral .It is known that the points $ O,M,Np$ are distinct. Prove that the points $ O,N,A,C$ are concyclic if and only if the points $ O,M,B,D$ are concyclic.

Proposer: Dorian Croitoru
9 replies
DreamTeam
Aug 14, 2008
AylyGayypow009
2 hours ago
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cubefree divisibility
DottedCaculator   63
N 2 hours ago by Assassino9931
Source: 2021 ISL N1
Find all positive integers $n\geq1$ such that there exists a pair $(a,b)$ of positive integers, such that $a^2+b+3$ is not divisible by the cube of any prime, and $$n=\frac{ab+3b+8}{a^2+b+3}.$$
63 replies
DottedCaculator
Jul 12, 2022
Assassino9931
2 hours ago
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$n$ with $2000$ divisors divides $2^n+1$ (IMO 2000)
Valentin Vornicu   67
N 2 hours ago by alexanderchew
Source: IMO 2000, Problem 5, IMO Shortlist 2000, Problem N3
Does there exist a positive integer $ n$ such that $ n$ has exactly 2000 prime divisors and $ n$ divides $ 2^n + 1$?
67 replies
Valentin Vornicu
Oct 24, 2005
alexanderchew
2 hours ago
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Hard Number Theory
MuradSafarli   1
N 2 hours ago by MR.1
Find all odd natural numbers \( m \) such that \( m^2 - 1 \mid 3^m + 5^m \).
1 reply
MuradSafarli
Yesterday at 7:06 PM
MR.1
2 hours ago
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most bruh geo you can imagineeeeeeeeeeeeee
ItzsleepyXD   0
2 hours ago
Source: bruhhhhhh
Let $ABC$ be triangle with $AC>AB$ and $B'$ on the segment $AC$ such that $AB=AB'$ . Consider point $E,F$ on $AB,AC$ such that $EF \parallel BB'$ . Point $T$ is the intersection of tangent line through point $E,F$ to circle $(EBC),(FBC)$ respectively . If the tangent through point $B'$ to $(BB'C)$ intersect $AB$ at $K$ . Line $KT$ intersect $BC$ at $D$ . Prove that $AD$ bisect $\angle BAC$ .
0 replies
ItzsleepyXD
2 hours ago
0 replies
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Combinatorial Double Sum
P162008   0
Apr 24, 2025
Compute $\sum_{r=0}^{n} \sum_{k=0}^{r} (-1)^k (k + 1)(k + 2) \binom {n + 5}{r - k}$
0 replies
P162008
Apr 24, 2025
0 replies
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Combinatorial Double Sum
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P162008
211 posts
P162008
#1 h  Apr 24, 2025, 1:03 AM
Y by
Compute $\sum_{r=0}^{n} \sum_{k=0}^{r} (-1)^k (k + 1)(k + 2) \binom {n + 5}{r - k}$
This post has been edited 1 time. Last edited by P162008, Apr 25, 2025, 3:25 AM
Reason: Typo
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