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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
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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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This shouldn't be a problem 15
derekli   1
N 8 minutes ago by Shan3t
Hey guys I was practicing AIME and came across this problem which is definitely misplaced. It asks for the surface area of a plane within a cylinder which we can easily find out using a projection that is easy to find. I think this should be placed in problem 10 or below. What do you guys think?
1 reply
+1 w
derekli
12 minutes ago
Shan3t
8 minutes ago
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Number Theory
fasttrust_12-mn   9
N 12 minutes ago by Shiny_zubat
Source: Pan African Mathematics Olympiad P1
Find all positive intgers $a,b$ and $c$ such that $\frac{a+b}{a+c}=\frac{b+c}{b+a}$ and $ab+bc+ca$ is a prime number
9 replies
1 viewing
fasttrust_12-mn
Aug 15, 2024
Shiny_zubat
12 minutes ago
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Interesting inequalities
sqing   5
N 16 minutes ago by sqing
Source: Own
Let $ a,b> 0 $ and $ a^2+ab+b^2=a+b $. Prove that
$$ \frac{a }{2b^2+1}+ \frac{b }{2a^2+1}+ \frac{1}{2ab+1} \geq \frac{21}{17}$$Let $ a,b> 0 $ and $ a^2+ab+b^2=a+b+1 $. Prove that
$$ \frac{a }{2b^2+1}+ \frac{b }{2a^2+1}+ \frac{1}{2ab+1} \geq1$$
5 replies
1 viewing
sqing
May 4, 2025
sqing
16 minutes ago
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3-var inequality
sqing   4
N 17 minutes ago by sqing
Source: Own
Let $ a,b,c\geq 0 ,a+b+c =1. $ Prove that
$$\frac{ab}{2c+1} +\frac{bc}{2a+1} +\frac{ca}{2b+1}+\frac{27}{20} abc\leq \frac{1}{4} $$
4 replies
sqing
May 3, 2025
sqing
17 minutes ago
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A Collection of Good Problems from my end
SomeonecoolLovesMaths   16
N 29 minutes ago by SomeonecoolLovesMaths
This is a collection of good problems and my respective attempts to solve them. I would like to encourage everyone to post their solutions to these problems, if any. This will not only help others verify theirs but also perhaps bring forward a different approach to the problem. I will constantly try to update the pool of questions.

The difficulty level of these questions vary from AMC 10 to AIME. (Although the main pool of questions were prepared as a mock test for IOQM over the years)

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5
16 replies
SomeonecoolLovesMaths
May 4, 2025
SomeonecoolLovesMaths
29 minutes ago
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Inequalities
sqing   9
N 34 minutes ago by sqing
Let $ a,b,c>0 $ and $ a+b\leq 16abc. $ Prove that
$$ a+b+kc^3\geq\sqrt[4]{\frac{4k} {27}}$$$$ a+b+kc^4\geq\frac{5} {8}\sqrt[5]{\frac{k} {2}}$$Where $ k>0. $
$$ a+b+3c^3\geq\sqrt{\frac{2} {3}}$$$$ a+b+2c^4\geq \frac{5} {8}$$
9 replies
1 viewing
sqing
May 4, 2025
sqing
34 minutes ago
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Incentre-excentre geometry
oVlad   1
N 37 minutes ago by mashumaro
Source: Romania Junior TST 2025 Day 2 P2
Consider a scalene triangle $ABC$ with incentre $I$ and excentres $I_a,I_b,$ and $I_c$, opposite the vertices $A,B,$ and $C$ respectively. The incircle touches $BC,CA,$ and $AB$ at $E,F,$ and $G$ respectively. Prove that the circles $IEI_a,IFI_b,$ and $IGI_c$ have a common point other than $I$.
1 reply
oVlad
2 hours ago
mashumaro
37 minutes ago
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IMO Genre Predictions
ohiorizzler1434   53
N 42 minutes ago by GreekIdiot
Everybody, with IMO upcoming, what are you predictions for the problem genres?


Personally I predict: predict
53 replies
1 viewing
ohiorizzler1434
May 3, 2025
GreekIdiot
42 minutes ago
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Functional Equation Problem
LeatuyrBertyk   0
an hour ago
Find all function $f:\mathbb{R}\to\mathbb{R}$ such that:
i) $f(x+y)\leq f(x)+f(y),\forall x,y\in\mathbb{R}$;
ii) $\ln 2025\cdot f(x)\leq 2025^x-1,\forall x\in\mathbb{R}$.
0 replies
LeatuyrBertyk
an hour ago
0 replies
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Two equal angles
jayme   5
N an hour ago by Captainscrubz
Dear Mathlinkers,

1. ABCD a square
2. I the midpoint of AB
3. 1 the circle center at A passing through B
4. Q the point of intersection of 1 with the segment IC
5. X the foot of the perpendicular to BC from Q
6. Y the point of intersection of 1 with the segment AX
7. M the point of intersection of CY and AB.

Prove : <ACI = <IYM.

Sincerely
Jean-Louis
5 replies
jayme
May 2, 2025
Captainscrubz
an hour ago
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Geometry
Lukariman   1
N an hour ago by Lukariman
Given circle (O) and point P outside (O). From P draw tangents PA and PB to (O) with contact points A, B. On the opposite ray of ray BP, take point M. The circle circumscribing triangle APM intersects (O) at the second point D. Let H be the projection of B on AM. Prove that <HDM = 2∠AMP.
1 reply
Lukariman
2 hours ago
Lukariman
an hour ago
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5-th powers is a no-go - JBMO Shortlist
WakeUp   7
N an hour ago by Namisgood
Prove that there are are no positive integers $x$ and $y$ such that $x^5+y^5+1=(x+2)^5+(y-3)^5$.

Note
7 replies
WakeUp
Oct 30, 2010
Namisgood
an hour ago
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positive integers forming a perfect square
cielblue   5
N an hour ago by Assassino9931
Find all positive integers $n$ such that $2^n-n^2+1$ is a perfect square.
5 replies
cielblue
May 2, 2025
Assassino9931
an hour ago
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geometry
JetFire008   2
N 2 hours ago by sunken rock
Given four concyclic points. For each subset of three points take the incenter. Show that the four incentres form a rectangle.
2 replies
JetFire008
Yesterday at 4:14 PM
sunken rock
2 hours ago
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J
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Three variables inequality
Headhunter   6
N Apr 30, 2025 by lbh_qys
$\forall a\in R$ ,$~\forall b\in R$ ,$~\forall c \in R$
Prove that at least one of $(a-b)^{2}$, $(b-c)^{2}$, $(c-a)^{2}$ is not greater than $\frac{a^{2}+b^{2}+c^{2}}{2}$.

I assume that all are greater than it, but can't go more.
6 replies
Headhunter
Apr 20, 2025
lbh_qys
Apr 30, 2025
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Three variables inequality
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Reveal topic tags
inequalities
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Headhunter
1963 posts
Headhunter
#1 h  Apr 20, 2025, 6:58 AM
Y by
$\forall a\in R$ ,$~\forall b\in R$ ,$~\forall c \in R$
Prove that at least one of $(a-b)^{2}$, $(b-c)^{2}$, $(c-a)^{2}$ is not greater than $\frac{a^{2}+b^{2}+c^{2}}{2}$.

I assume that all are greater than it, but can't go more.
Z K Y
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programjames1
3046 posts
programjames1
#2 h  Apr 20, 2025, 7:20 AM
Y by
Can you give the reference? I think this is from a USAJMO contest in the 2010s.

EDIT: I was thinking of USA(J)MO 2018 #1 (#2) which can be rearranged to a similar inequality.
This post has been edited 2 times. Last edited by programjames1, Apr 20, 2025, 7:23 AM
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Headhunter
1963 posts
Headhunter
#3 h  Apr 20, 2025, 9:01 AM
Y by
I guess that this problem is from chinese materials at 1990~2004. but I'm not sure. Thanks.
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lbh_qys
558 posts
lbh_qys
#4 h  Apr 21, 2025, 3:04 AM
Y by
Hint
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lbh_qys
558 posts
lbh_qys
#5 h  Apr 21, 2025, 3:18 AM • 2 Y
Y by programjames1, spy27
another solution
This post has been edited 1 time. Last edited by lbh_qys, Apr 21, 2025, 3:18 AM
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spy27
8 posts
spy27
#6 h  Apr 30, 2025, 5:38 AM
Y by
lbh_qys wrote:
another solution

Can you explain the \( a + b + c \neq 0 \) case in some detail?
Z K Y
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lbh_qys
558 posts
lbh_qys
#7 h  Apr 30, 2025, 6:08 AM
Y by
spy27 wrote:
lbh_qys wrote:
another solution

Can you explain the \( a + b + c \neq 0 \) case in some detail?

$f(x) = (a+x)^2 + (b+x)^2 + (c+x)^2 $ get minimum at $x=0$ iff $a+b+c=0$.
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