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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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Inequalities
sqing   2
N a few seconds ago by DAVROS
Let $a,b,c >2 $ and $ ab+bc+ca \leq 75.$ Show that
$$\frac{1}{a-2}+\frac{1}{b-2}+\frac{1}{c-2}\geq 1$$Let $a,b,c >2 $ and $ \frac{1}{a}+\frac{1}{b}+\frac{1}{c}\geq \frac{6}{7}.$ Show that
$$\frac{1}{a-2}+\frac{1}{b-2}+\frac{1}{c-2}\geq 2$$
2 replies
sqing
Yesterday at 11:31 AM
DAVROS
a few seconds ago
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inequality
xytunghoanh   5
N 25 minutes ago by lbh_qys
For $a,b,c\ge 0$. Let $a+b+c=3$.
Prove or disprove
\[\sum ab +\sum ab^2 \le 6\]
5 replies
xytunghoanh
4 hours ago
lbh_qys
25 minutes ago
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Interesting inequality of sequence
GeorgeRP   0
25 minutes ago
Source: Bulgaria IMO TST 2025 P2
Let $d\geq 2$ be an integer and $a_0,a_1,\ldots$ is a sequence of real numbers for which $a_0=a_1=\cdots=a_d=1$ and:
$$a_{k+1}\geq a_k-\frac{a_{k-d}}{4d}, \forall_{k\geq d}$$Prove that all elements of the sequence are positive.
0 replies
1 viewing
GeorgeRP
25 minutes ago
0 replies
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Parallel lines in incircle configuration
GeorgeRP   0
27 minutes ago
Source: Bulgaria IMO TST 2025 P1
Let $I$ be the incenter of triangle $\triangle ABC$. Let $H_A$, $H_B$, and $H_C$ be the orthocenters of triangles $\triangle BCI$, $\triangle ACI$, and $\triangle ABI$, respectively. Prove that the lines through $H_A$, $H_B$, and $H_C$, parallel to $AI$, $BI$, and $CI$, respectively, are concurrent.
0 replies
GeorgeRP
27 minutes ago
0 replies
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Expensive n-tuples
jlammy   28
N 37 minutes ago by Jupiterballs
Source: EGMO 2017 P5
Let $n\geq2$ be an integer. An $n$-tuple $(a_1,a_2,\dots,a_n)$ of not necessarily different positive integers is expensive if there exists a positive integer $k$ such that $$(a_1+a_2)(a_2+a_3)\dots(a_{n-1}+a_n)(a_n+a_1)=2^{2k-1}.$$a) Find all integers $n\geq2$ for which there exists an expensive $n$-tuple.

b) Prove that for every odd positive integer $m$ there exists an integer $n\geq2$ such that $m$ belongs to an expensive $n$-tuple.

There are exactly $n$ factors in the product on the left hand side.


28 replies
jlammy
Apr 9, 2017
Jupiterballs
37 minutes ago
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Assam Mathematics Olympiad 2022 Category III Q17
SomeonecoolLovesMaths   1
N an hour ago by nyacide
Consider a rectangular grid of points consisting of $4$ rows and $84$ columns. Each point is coloured with one of the colours red, blue or green. Show that no matter whatever way the colouring is done, there always exist four points
of the same colour that form the vertices of a rectangle. An illustration is shown in the figure below.
1 reply
SomeonecoolLovesMaths
Sep 12, 2024
nyacide
an hour ago
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Equal areas of the triangles on the parabola
NO_SQUARES   1
N an hour ago by Photaesthesia
Source: Regional Stage of ARO 2025 10.10; also Kvant 2025 no. 3 M2837
On the graphic of the function $y=x^2$ were selected $1000$ pairwise distinct points, abscissas of which are integer numbers from the segment $[0; 100000]$. Prove that it is possible to choose six different selected points $A$, $B$, $C$, $A'$, $B'$, $C'$ such that areas of triangles $ABC$ and $A'B'C'$ are equals.
A. Tereshin
1 reply
NO_SQUARES
Yesterday at 7:41 PM
Photaesthesia
an hour ago
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forced vertices in graphs
Davdav1232   2
N an hour ago by Davdav1232
Source: Israel TST 7 2025 p2
Let \( G \) be a graph colored using \( k \) colors. We say that a vertex is forced if it has neighbors in all the other \( k - 1 \) colors.

Prove that for any \( 2024 \)-regular graph \( G \) that contains no triangles or quadrilaterals, there exists a coloring using \( 2025 \) colors such that at least \( 1013 \) of the colors have a forced vertex of that color.

Note: The graph coloring must be valid, this means no \( 2 \) vertices of the same color may be adjacent.
2 replies
1 viewing
Davdav1232
May 8, 2025
Davdav1232
an hour ago
J
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Inequalities
sqing   6
N an hour ago by DAVROS
Let $a,b,c >1 $ and $ \frac{1}{a-1}+\frac{1}{b-1}+\frac{1}{c-1}=1.$ Show that$$ab+bc+ca \geq 48$$$$\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\leq \frac{3}{4}$$Let $a,b,c >1 $ and $ \frac{1}{a-1}+\frac{1}{b-1}+\frac{1}{c-1}=2.$ Show that$$ab+bc+ca \geq \frac{75}{4}$$$$\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\leq \frac{6}{5}$$Let $a,b,c >1 $ and $ \frac{1}{a-1}+\frac{1}{b-1}+\frac{1}{c-1}=3.$ Show that$$ab+bc+ca \geq 12$$$$\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\leq \frac{3}{2}$$
6 replies
sqing
Yesterday at 9:04 AM
DAVROS
an hour ago
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Transposition?
EeEeRUT   0
an hour ago
Source: Thailand MO 2025 P8
For each integer sequence $a_1, a_2, a_3, \dots, a_n$, a single parity swapping is to choose $2$ terms in this sequence, say $a_i$ and $a_j$, such that $a_i + a_j$ is odd, then switch their placement, while the other terms stay in place. This creates a new sequence.

Find the minimal number of single parity swapping to transform the sequence $1,2,3, \dots, 2025$ to $2025, \dots, 3, 2, 1$, using only single parity swapping.
0 replies
EeEeRUT
an hour ago
0 replies
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Assam Mathematics Olympiad 2022 Category III Q14
SomeonecoolLovesMaths   1
N an hour ago by nyacide
The following sum of three four digits numbers is divisible by $75$, $7a71 + 73b7 + c232$, where $a, b, c$ are decimal digits. Find the necessary conditions in $a, b, c$.
1 reply
SomeonecoolLovesMaths
Sep 12, 2024
nyacide
an hour ago
J
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Some number theory
EeEeRUT   0
an hour ago
Source: Thailand MO 2025 P9
Let $p$ be an odd prime and $S = \{1,2,3,\dots, p\}$
Assume that $U: S \rightarrow S$ is a bijection and $B$ is an integer such that $$B\cdot U(U(a)) - a \: \text{ is a multiple of} \: p \: \text{for all} \: a \in S$$Show that $B^{\frac{p-1}{2}} -1$ is a multiple of $p$.
0 replies
EeEeRUT
an hour ago
0 replies
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help me please,thanks
tnhan.129   1
N an hour ago by pco
find f: R+ -> R such that:
f(x)/x + f(y)/y = (1/x + 1/y).f(sqrt(xy))
1 reply
tnhan.129
May 11, 2025
pco
an hour ago
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What is thiss
EeEeRUT   0
an hour ago
Source: Thailand MO 2025 P6
Find all function $f: \mathbb{R}^+ \rightarrow \mathbb{R}$,such that the inequality $$f(x) + f(\frac{y}{x}) \leqslant \frac{x^3}{y^2} + \frac{y}{x^3}$$holds for all positive reals $x,y$ and for every positive real $x$, there exist positive reals $y$, such that the equality holds.
0 replies
EeEeRUT
an hour ago
0 replies
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100th post
MathJedi108   1
N Apr 20, 2025 by mdk2013
Well I guess this is my 100th post, it would be really funny if it isn't can yall share your favorite experience on AoPS here?
1 reply
MathJedi108
Apr 20, 2025
mdk2013
Apr 20, 2025
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100th post
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Reveal topic tags
100th Post
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MathJedi108
100 posts
MathJedi108
#1 h  Apr 20, 2025, 10:59 PM
Y by
Well I guess this is my 100th post, it would be really funny if it isn't can yall share your favorite experience on AoPS here?
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mdk2013
642 posts
mdk2013
#2 h  Apr 20, 2025, 11:10 PM
Y by
why is this post in hsm though
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