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k a March Highlights and 2025 AoPS Online Class Information
jlacosta   0
Mar 2, 2025
March is the month for State MATHCOUNTS competitions! Kudos to everyone who participated in their local chapter competitions and best of luck to all going to State! Join us on March 11th for a Math Jam devoted to our favorite Chapter competition problems! Are you interested in training for MATHCOUNTS? Be sure to check out our AMC 8/MATHCOUNTS Basics and Advanced courses.

Are you ready to level up with Olympiad training? Registration is open with early bird pricing available for our WOOT programs: MathWOOT (Levels 1 and 2), CodeWOOT, PhysicsWOOT, and ChemWOOT. What is WOOT? WOOT stands for Worldwide Online Olympiad Training and is a 7-month high school math Olympiad preparation and testing program that brings together many of the best students from around the world to learn Olympiad problem solving skills. Classes begin in September!

Do you have plans this summer? There are so many options to fit your schedule and goals whether attending a summer camp or taking online classes, it can be a great break from the routine of the school year. Check out our summer courses at AoPS Online, or if you want a math or language arts class that doesn’t have homework, but is an enriching summer experience, our AoPS Virtual Campus summer camps may be just the ticket! We are expanding our locations for our AoPS Academies across the country with 15 locations so far and new campuses opening in Saratoga CA, Johns Creek GA, and the Upper West Side NY. Check out this page for summer camp information.

Be sure to mark your calendars for the following events:
[list][*]March 5th (Wednesday), 4:30pm PT/7:30pm ET, HCSSiM Math Jam 2025. Amber Verser, Assistant Director of the Hampshire College Summer Studies in Mathematics, will host an information session about HCSSiM, a summer program for high school students.
[*]March 6th (Thursday), 4:00pm PT/7:00pm ET, Free Webinar on Math Competitions from elementary through high school. Join us for an enlightening session that demystifies the world of math competitions and helps you make informed decisions about your contest journey.
[*]March 11th (Tuesday), 4:30pm PT/7:30pm ET, 2025 MATHCOUNTS Chapter Discussion MATH JAM. AoPS instructors will discuss some of their favorite problems from the MATHCOUNTS Chapter Competition. All are welcome!
[*]March 13th (Thursday), 4:00pm PT/7:00pm ET, Free Webinar about Summer Camps at the Virtual Campus. Transform your summer into an unforgettable learning adventure! From elementary through high school, we offer dynamic summer camps featuring topics in mathematics, language arts, and competition preparation - all designed to fit your schedule and ignite your passion for learning.[/list]
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0 replies
jlacosta
Mar 2, 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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Isogonal conjugates
drmzjoseph   4
N 11 minutes ago by Geometrylife
Source: Maybe own
Let $ABC$ a triangle with circumcircle $\Gamma$ and isogonal conjugates $P$ and $Q$. Take $X$ and $Y$ points on $AB$ and $BC$ respectively such that $\angle PXA=\angle CYQ$. If $\odot(PXA)$ cut $\Gamma$ again at $R$. Prove that $RY$ and $QA$ cut at $\Gamma$

If $P$ and $Q$ are external just read it by directed angles
Btw i found this using well-known lemma so it might not be mine
4 replies
drmzjoseph
Mar 10, 2025
Geometrylife
11 minutes ago
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Combinatorics Geometry
Wasdshift   0
31 minutes ago
Source: 2011 All-Russian MO Regional Grade 9 P3
“A closed non-self-intersecting polygonal chain is drawn through the centers of some squares on the $8\times 8$ chess board. Every link of the chain connects the centers of adjacent squares either horizontally, vertically or diagonally, where the two squares are adjacent if they share an edge or a corner. For the interior polygon bounded by the chain, prove that the total area of black pieces equals the total area of white pieces. “
Can I have a hint for this problem please?
Click to reveal hidden text
0 replies
Wasdshift
31 minutes ago
0 replies
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SONG circle?
YaoAOPS   0
33 minutes ago
Source: own?
Let triangle $ABC$ have incenter $I$ and intouch triangle $DEF$. Let the circumcircle of $ABC$ intersect $(AEF)$ at $S$ and have center $O$. Let $N$ be the midpoint of arc $BAC$ on the circumcircle. Suppose quadrilateral $SONG$ is cyclic such that $X = SN \cap OG$ lies on $BC$. Show that $\angle XGD = 90^\circ$.
0 replies
YaoAOPS
33 minutes ago
0 replies
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9 Three concurrent chords
v_Enhance   4
N 36 minutes ago by cosmicgenius
Three distinct circles $\Omega_1$, $\Omega_2$, $\Omega_3$ cut three common chords concurrent at $X$. Consider two distinct circles $\Gamma_1$, $\Gamma_2$ which are internally tangent to all $\Omega_i$. Determine, with proof, which of the following two statements is true.

(1) $X$ is the insimilicenter of $\Gamma_1$ and $\Gamma_2$
(2) $X$ is the exsimilicenter of $\Gamma_1$ and $\Gamma_2$.
4 replies
v_Enhance
Yesterday at 8:45 PM
cosmicgenius
36 minutes ago
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Integral with dt
RenheMiResembleRice   2
N 37 minutes ago by RenheMiResembleRice
Source: Yanxue Lu
Solve the attached:
2 replies
RenheMiResembleRice
4 hours ago
RenheMiResembleRice
37 minutes ago
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Show these 2 circles are tangent to each other.
MTA_2024   1
N 38 minutes ago by MTA_2024
A, B, C, and O are four points in the plane such that
\(\angle ABC > 90^\circ\)
and
\( OA = OB = OC \).

Let \( D \) be a point on \( (AB) \), and let \( (d) \) be a line passing through \( D \) such that
\( (AC) \perp (DC) \)
and
\( (d) \perp (AO) \).

The line \( (d) \) intersects \( (AC) \) at \( E \) and the circumcircle of triangle \( ABC \) at \( F \) (\( F \neq A \)).

Show that the circumcircles of triangles \( BEF \) and \( CFD \) are tangent at \( F \).
1 reply
MTA_2024
Yesterday at 1:12 PM
MTA_2024
38 minutes ago
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Inequality with real numbers
JK1603JK   0
39 minutes ago
Source: unknown
Let a,b,c are real numbers. Prove that (a^3+b^3+c^3+3abc)^4+(a+b+c)^3(a+b-c)^3(-a+b+c)^3(a-b+c)^3>=0
0 replies
JK1603JK
39 minutes ago
0 replies
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Find min
hunghd8   7
N an hour ago by hunghd8
Let $a,b,c$ be nonnegative real numbers such that $ a+b+c\geq 2+abc $. Find min
$$P=a^2+b^2+c^2.$$
7 replies
hunghd8
Yesterday at 12:10 PM
hunghd8
an hour ago
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inequality marathon
EthanWYX2009   190
N an hour ago by EthanWYX2009
There is an inequality marathon now, but the problem is too hard for me to solve, let's start a new one here, please post problems that is not too difficult.
------
P1.
Find the maximum value of ${M}$, such that for $\forall a,b,c\in\mathbb R_+,$
$$a^3+b^3+c^3-3abc\geqslant M(a^2b+b^2c+c^2a-3abc).$$
190 replies
EthanWYX2009
May 21, 2023
EthanWYX2009
an hour ago
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Find interger root
Zuyong   1
N an hour ago by Zuyong
Source: ?
Find $(k,m)\in \mathbb{Z}$ satisfying $$9 k^4 + 30 k^3 + 44 k^2 m + 105 k^2 + 20 k m - 120 k + 36 m^2 + 80 m - 240=0$$
1 reply
Zuyong
Oct 24, 2024
Zuyong
an hour ago
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hard..........
Noname23   0
2 hours ago
problem
0 replies
Noname23
2 hours ago
0 replies
J
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Geometry solutions needed of pathfinder senior
SHIVAM_OP-IMO2025   1
N 2 hours ago by S.Ragnork1729
Someone plzz share pathfinder senior by vikas tiwari solutions..
1 reply
SHIVAM_OP-IMO2025
2 hours ago
S.Ragnork1729
2 hours ago
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new playlist in Olympiad Geometry Channel
Plane_geometry_youtuber   3
N 2 hours ago by SHIVAM_OP-IMO2025
Hi,

I create a new playlist called "Problems from Audience". I will put my solution of the problems from audience into this playlist. Welcome to send me your problems and doubts.

https://www.youtube.com/@OlympiadGeometry-2024

my email: planery.geometry@gmail.com
3 replies
Plane_geometry_youtuber
Jan 28, 2025
SHIVAM_OP-IMO2025
2 hours ago
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Prove that $\angle FAC = \angle EDB$
micliva   26
N 2 hours ago by cappucher
Source: All-Russian Olympiad 1996, Grade 10, First Day, Problem 1
Points $E$ and $F$ are given on side $BC$ of convex quadrilateral $ABCD$ (with $E$ closer than $F$ to $B$). It is known that $\angle BAE = \angle CDF$ and $\angle EAF = \angle FDE$. Prove that $\angle FAC = \angle EDB$.

M. Smurov
26 replies
micliva
Apr 18, 2013
cappucher
2 hours ago
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Find the number of integral solutions
Mathlover08092002   1
N Thursday at 9:15 AM by quasar_lord
Source: MTRP 2019 Class 11-Multiple Choice Question: Problem 2 :-
What is the number of integral solutions of the equation $a^{b^2}=b^{2a}$, where a > 0 and $|b|>|a|$
[list=1]
[*] 3
[*] 4
[*] 6
[*] 8
[/list]
1 reply
Mathlover08092002
Apr 9, 2020
quasar_lord
Thursday at 9:15 AM
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Find the number of integral solutions
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Reveal topic tags
number theory
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Source: MTRP 2019 Class 11-Multiple Choice Question: Problem 2 :-
The post below has been deleted. Click to close.
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Mathlover08092002
408 posts
Mathlover08092002
#1 h  Apr 9, 2020, 4:40 PM • 1 Y
Y by Mango247
What is the number of integral solutions of the equation $a^{b^2}=b^{2a}$, where a > 0 and $|b|>|a|$
  1. 3
  2. 4
  3. 6
  4. 8
This post has been edited 1 time. Last edited by Mathlover08092002, Apr 10, 2020, 7:52 PM
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The post below has been deleted. Click to close.
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quasar_lord
174 posts
quasar_lord
#2 h  Thursday at 9:15 AM
Y by
bump? 8char
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