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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)!

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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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2024 Japan Mathematical Olympiad Preliminary
parkjungmin   0
2 minutes ago
2024 Japan Mathematical Olympiad Preliminary
0 replies
parkjungmin
2 minutes ago
0 replies
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ISI UGB 2025 P2
SomeonecoolLovesMaths   8
N 12 minutes ago by lakshya2009
Source: ISI UGB 2025 P2
If the interior angles of a triangle $ABC$ satisfy the equality, $$\sin ^2 A + \sin ^2 B + \sin^2 C = 2 \left( \cos ^2 A + \cos ^2 B + \cos ^2 C \right),$$prove that the triangle must have a right angle.
8 replies
SomeonecoolLovesMaths
Yesterday at 11:16 AM
lakshya2009
12 minutes ago
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2025 Japanese Mathematics Olympiad
parkjungmin   0
16 minutes ago
2025 Japanese Mathematics Olympiad
0 replies
+1 w
parkjungmin
16 minutes ago
0 replies
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Points on the sides of cyclic quadrilateral satisfy the angle conditions
AlperenINAN   3
N 25 minutes ago by Primeniyazidayi
Source: Turkey JBMO TST 2025 P1
Let $ABCD$ be a cyclic quadrilateral and let the intersection point of lines $AB$ and $CD$ be $E$. Let the points $K$ and $L$ be arbitrary points on sides $CD$ and $AB$ respectively, which satisfy the conditions
$$\angle KAD = \angle KBC \quad \text{and} \quad \angle LDA = \angle LCB.$$Prove that $EK = EL$.
3 replies
AlperenINAN
Yesterday at 7:15 PM
Primeniyazidayi
25 minutes ago
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Calculating sum of the numbers
Sadigly   4
N 25 minutes ago by MITDragon
Source: Azerbaijan Junior MO 2025 P4
A $3\times3$ square is filled with numbers $1;2;3...;9$.The numbers inside four $2\times2$ squares is summed,and arranged in an increasing order. Is it possible to obtain the following sequences as a result of this operation?

$\text{a)}$ $24,24,25,25$

$\text{b)}$ $20,23,26,29$
4 replies
Sadigly
May 9, 2025
MITDragon
25 minutes ago
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Inequality
Sadigly   8
N an hour ago by Sadigly
Source: Azerbaijan Junior MO 2025 P5
For positive real numbers $x;y;z$ satisfying $0<x,y,z<2$, find the biggest value the following equation could acquire:


$$(2x-yz)(2y-zx)(2z-xy)$$
8 replies
Sadigly
May 9, 2025
Sadigly
an hour ago
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Minimum value of a 3 variable expression
bin_sherlo   5
N an hour ago by Primeniyazidayi
Source: Türkiye 2025 JBMO TST P6
Find the minimum value of
\[\frac{x^3+1}{(y-1)(z+1)}+\frac{y^3+1}{(z-1)(x+1)}+\frac{z^3+1}{(x-1)(y+1)}\]where $x,y,z>1$ are reals.
5 replies
+1 w
bin_sherlo
Yesterday at 7:16 PM
Primeniyazidayi
an hour ago
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Nice R+ FE
math_comb01   5
N an hour ago by jasperE3
Source: XOOK 2025 P3
Find all functions $f : \mathbb{R}_{>0} \to \mathbb{R}_{>0}$ so that for any $x, y \in \mathbb{R}_{>0}$, we have \[ f(xf(x^2)+yf(x))=xf(y+xf(x)). \]
Proposed by Anmol Tiwari and MathLuis
5 replies
+1 w
math_comb01
Feb 9, 2025
jasperE3
an hour ago
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2n^2+4n-1 and 3n+4 have common powers
bin_sherlo   3
N an hour ago by Primeniyazidayi
Source: Türkiye 2025 JBMO TST P5
Find all positive integers $n$ such that a positive integer power of $2n^2+4n-1$ equals to a positive integer power of $3n+4$.
3 replies
bin_sherlo
Yesterday at 7:13 PM
Primeniyazidayi
an hour ago
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Help me solve this problem please. Thank you so much!
illybest   1
N an hour ago by GreekIdiot
Give two fixed points B and C, and point A moving on the circle (O). Let D be a point on (O) such that AD is perpendicular to BC. Let O' be the point symmetric to O with respect to BC, M be the midpoint of BC, and N ( dinstinct from D) be the intersection of MD with the circumcircle of triangle AOD. Suppose DO' intersects the circle (O) again at S.
a) Prove that the circle (OMN) is tangent to the circle (DNS)
b) Let d be the line tangent to (DNS) at N. Prove that d always passes through a fixed point when A moves along the arc BC of (O)
1 reply
illybest
Sep 8, 2024
GreekIdiot
an hour ago
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Looks like power mean, but it is not
Nuran2010   6
N an hour ago by sqing
Source: Azerbaijan Al-Khwarizmi IJMO TST 2025
For $a,b,c$ positive real numbers satisfying $a^2+b^2+c^2 \geq 3$,show that:

$\sqrt[3]{\frac{a^3+b^3+c^3}{3}}+\frac{a+b+c}{9} \geq \frac{4}{3}$.
6 replies
Nuran2010
Yesterday at 11:51 AM
sqing
an hour ago
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Expressing polynomial as product of two polynomials
Sadigly   5
N 2 hours ago by Sadigly
Source: Azerbaijan Senior NMO 2021
Define $P(x)=((x-a_1)(x-a_2)...(x-a_n))^2 +1$, where $a_1,a_2...,a_n\in\mathbb{Z}$ and $n\in\mathbb{N^+}$. Prove that $P(x)$ couldn't be expressed as product of two non-constant polynomials with integer coefficients.
5 replies
Sadigly
Yesterday at 9:10 PM
Sadigly
2 hours ago
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Simple inequality
sqing   19
N 2 hours ago by sqing
Source: Old? Where?
Let $a,b,c$ be positive real numbers .Prove that
$$(a+b)^2+(a+b+4c)^2\geq \frac{100 abc}{a+b+c}$$
19 replies
sqing
Jan 16, 2021
sqing
2 hours ago
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Interesting inequalities
sqing   2
N 2 hours ago by sqing
Source: Own
Let $ a,b>0 $ . Prove that
$$ \frac{a^2+b^2}{ab+1}+ \frac{4}{ (\sqrt{a}+\sqrt{b})^2} \geq 2$$$$ \frac{a^2+b^2}{ab+1}+ \frac{3}{a+\sqrt{ab}+b} \geq 2$$$$ \frac{a^3+b^3}{ab+1}+ \frac{4}{(a+b)^2} \geq 2$$$$ \frac{a^3+b^3}{ab+1}+ \frac{3}{a^2+ab+b^2} \geq 2$$$$\frac{a^2+b^2}{ab+2}+ \frac{1}{2\sqrt{ab}} \geq \frac{2+3\sqrt{2}-2\sqrt{2(\sqrt{2}-1)}}{4} $$
2 replies
sqing
Today at 4:34 AM
sqing
2 hours ago
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convex ABCD, AB=CB, <ABC +2<CDA = \pi, AE=EC, prove <CDE=<BDA
parmenides51   1
N Sep 26, 2018 by little-fermat
Source: IMAR 2009 p3
Consider a convex quadrilateral $ABCD$ with $AB=CB$ and $\angle ABC +2 \angle CDA = \pi$ and let $E$ be the midpoint of $AC$. Show that $\angle CDE =\angle BDA$.

Paolo Leonetti
1 reply
parmenides51
Sep 26, 2018
little-fermat
Sep 26, 2018
J
convex ABCD, AB=CB, <ABC +2<CDA = \pi, AE=EC, prove <CDE=<BDA
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Reveal topic tags
geometry
Angle Chasing
convex quadrilateral
angles
equal angles
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Source: IMAR 2009 p3
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parmenides51
30652 posts
parmenides51
#1 h  Sep 26, 2018, 7:33 PM • 1 Y
Y by Adventure10
Consider a convex quadrilateral $ABCD$ with $AB=CB$ and $\angle ABC +2 \angle CDA = \pi$ and let $E$ be the midpoint of $AC$. Show that $\angle CDE =\angle BDA$.

Paolo Leonetti
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The post below has been deleted. Click to close.
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little-fermat
147 posts
little-fermat
#2 h  Sep 26, 2018, 8:29 PM • 2 Y
Y by Adventure10, Mango247
Note that $B$ is the intersection of the tangents from $A,C$ to the circle $(ADC)$
So $DB$ is a symmedian in $\triangle ADC$ which implies the result .
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