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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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Functions
mclolikoi   2
N a few seconds ago by Moubinool
Let us consider f as the following function : $ f(x)= \frac {x - \sqrt{2}}{ [x \sqrt{2} ] } $

1- Find the definition domain $ D_f $

2-Prove that $ f $ is continous on $ \sqrt{2} $

3-Study the continuity of $ f $ on $ \frac {3 \sqrt{2} }{2} $

4-Then draw the geometric representation of $ f $ on $ ] \frac {1}{ \sqrt{2} } ; 2 \sqrt{2} [ $
2 replies
+1 w
mclolikoi
Sep 23, 2012
Moubinool
a few seconds ago
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Changing unordered triples
nAalniaOMliO   1
N an hour ago by FarrukhBurzu
Source: Belarusian National Olympiad 2023
An unordered triple of numbers $(a,b,c)$ in one move you can change to either $(a,b,2a+2b-c)$, $(a,2a+2c-b,c)$ or $(2b+2c-a,b,c)$.
Can you from the triple $(3,5,14)$ get the tripel $(3,13,6)$ in finite amount of moves?
1 reply
nAalniaOMliO
Dec 31, 2024
FarrukhBurzu
an hour ago
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prove that f is a second degree polynomial.
sqing   6
N an hour ago by Assassino9931
Source: Shortlist BMO 2018, A5
Let $f: \mathbb {R} \to \mathbb {R}$ be a concave function and $g: \mathbb {R} \to \mathbb {R}$ be a continuous function . If $$ f (x + y) + f (x-y) -2f (x) = g (x) y^2 $$for all $x, y \in \mathbb {R}, $ prove that $f $ is a second degree polynomial.
6 replies
sqing
May 3, 2019
Assassino9931
an hour ago
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Inspired by sadwinter
sqing   0
an hour ago
Source: Own
Let $ 0\leq a,b \leq1 $. Prove that
$$0\leq (a+2b)^2+ \frac{8}{3}a(a- 2b+ab^2)(3a^2+ b^2) \leq9$$$$0\leq (a+2b)^2+ \frac{3}{2}a^2(1-b^2)(3a^2+ b^2)\leq9$$$$0\leq(a+2b)^2+2a^2(1-b^2)(3a^2+ b^2) \leq7+\frac{3}{\sqrt[3]2}$$$$3\sqrt[3]2-\frac{13}{2} \leq (a+2b)^2+ \frac{8}{3}ab(ab- 2)(3a^2+ b^2) \leq 4$$
0 replies
1 viewing
sqing
an hour ago
0 replies
J
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Prove the statement
Butterfly   13
N an hour ago by solyaris
Given an infinite sequence $\{x_n\} \subseteq [0,1]$, there exists some constant $C$, for any $r>0$, among the sequence $x_n$ and $x_m$ could be chosen to satisfy $|n-m|\ge r $ and $|x_n-x_m|<\frac{C}{|n-m|}$.
13 replies
Butterfly
May 7, 2025
solyaris
an hour ago
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Points on a lattice path lies on a line
navi_09220114   5
N an hour ago by dgrozev
Source: TASIMO 2025 Day 1 Problem 3
Let $S$ be a nonempty subset of the points in the Cartesian plane such that for each $x\in S$ exactly one of $x+(0,1)$ or $x+(1,0)$ also belongs to $S$. Prove that for each positive integer $k$ there is a line in the plane (possibly different lines for different $k$) which contains at least $k$ points of $S$.
5 replies
navi_09220114
May 19, 2025
dgrozev
an hour ago
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Interesting divisors
Warideeb   0
an hour ago
Find all odd positive integer $n$ such that for any two co-prime positive integers $(a,b)$ if $ab|n$ then $a+b-1|n$.
0 replies
Warideeb
an hour ago
0 replies
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Nice problem
Martin.s   1
N an hour ago by cazanova19921
If \(p\) is a prime and \(n \geq p\), then
\[ n! \sum_{pi+j=n} \frac{1}{p^i i! j!} \equiv 0 \pmod{p}. \]
1 reply
Martin.s
Yesterday at 6:46 PM
cazanova19921
an hour ago
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Interesting geometry problem
DrAymeinstein   3
N 2 hours ago by Rayvhs
Source: Moroccan TST 2019 P6
Let $ABC$ be a triangle. The tangent in $A$ of the circumcircle of $ABC$ cuts the line $(BC)$ in $X$. Let $A'$ be the symetric of $A$ by $X$ and $C'$ the symetric of $C$ by the line $(AX)$
Prove that the points $A, C', A'$ and $B$ are concyclic.
3 replies
DrAymeinstein
Aug 23, 2024
Rayvhs
2 hours ago
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small problem
sadwinter   0
2 hours ago
Source: own
Let $0\leq a,b \leq1$. Prove that
$0\leq(a+2b)^2-4a(4b-a-3ab^2)(2a^2+b^2)\leq9$
0 replies
sadwinter
2 hours ago
0 replies
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Circle Midpoint Config
Fuyuki   0
2 hours ago
In triangle ABC, point D is the midpoint of BC. Let the second intersection of AD and (ABC) be E. Then, F is the intersection of EC and AB. G is the intersection of BE and AC. Prove that BC is parallel to FG.
0 replies
Fuyuki
2 hours ago
0 replies
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D1040 : A general and strange result
Dattier   1
N 2 hours ago by Dattier
Source: les dattes à Dattier
Let $f \in C([0,1];[0,1])$ bijective, $f(0)=0$ and $(a_k) \in [0,1]^\mathbb N$ with $ \sum \limits_{k=0}^{+\infty} a_k$ converge.

Is it true that $\sum \limits_{k=0}^{+\infty} \sqrt{f(a_k)\times f^{-1}(a_k)}$ converge?
1 reply
Dattier
Saturday at 12:46 PM
Dattier
2 hours ago
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IMO ShortList 2001, combinatorics problem 4
orl   13
N 3 hours ago by Aiden-1089
Source: IMO ShortList 2001, combinatorics problem 4
A set of three nonnegative integers $\{x,y,z\}$ with $x < y < z$ is called historic if $\{z-y,y-x\} = \{1776,2001\}$. Show that the set of all nonnegative integers can be written as the union of pairwise disjoint historic sets.
13 replies
orl
Sep 30, 2004
Aiden-1089
3 hours ago
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Limit problem
Martin.s   1
N 3 hours ago by alexheinis
Find \(\lim_{n \to \infty} n \sin (2n! e \pi)\)
1 reply
Martin.s
Yesterday at 6:49 PM
alexheinis
3 hours ago
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mqoi_KOLA   0
Apr 1, 2025
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mqoi_KOLA
Apr 1, 2025
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mqoi_KOLA
#1 h  Apr 1, 2025, 5:46 AM
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