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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.

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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!
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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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quadratics
luciazhu1105   20
N 6 minutes ago by KF329
I really need help on quadratics and I don't know why I also kinda need a bit of help on graphing functions and finding the domain and range of them.
20 replies
luciazhu1105
Feb 14, 2025
KF329
6 minutes ago
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A touching question on perpendicular lines
Tintarn   1
N an hour ago by Mathzeus1024
Source: Bundeswettbewerb Mathematik 2025, Round 1 - Problem 3
Let $k$ be a semicircle with diameter $AB$ and midpoint $M$. Let $P$ be a point on $k$ different from $A$ and $B$.

The circle $k_A$ touches $k$ in a point $C$, the segment $MA$ in a point $D$, and additionally the segment $MP$. The circle $k_B$ touches $k$ in a point $E$ and additionally the segments $MB$ and $MP$.

Show that the lines $AE$ and $CD$ are perpendicular.
1 reply
Tintarn
Mar 17, 2025
Mathzeus1024
an hour ago
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Inequality with ordering
JustPostChinaTST   7
N an hour ago by AshAuktober
Source: 2021 China TST, Test 1, Day 1 P1
Given positive integers $m$ and $n$. Let $a_{i,j} ( 1 \le i \le m, 1 \le j \le n)$ be non-negative real numbers, such that
$$ a_{i,1} \ge a_{i,2} \ge \cdots \ge a_{i,n} \text{ and } a_{1,j} \ge a_{2,j} \ge \cdots \ge a_{m,j} $$holds for all $1 \le i \le m$ and $1 \le j \le n$. Denote
$$ X_{i,j}=a_{1,j}+\cdots+a_{i-1,j}+a_{i,j}+a_{i,j-1}+\cdots+a_{i,1},$$$$ Y_{i,j}=a_{m,j}+\cdots+a_{i+1,j}+a_{i,j}+a_{i,j+1}+\cdots+a_{i,n}.$$Prove that
$$ \prod_{i=1}^{m} \prod_{j=1}^{n} X_{i,j} \ge \prod_{i=1}^{m} \prod_{j=1}^{n} Y_{i,j}.$$
7 replies
JustPostChinaTST
Mar 17, 2021
AshAuktober
an hour ago
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D1010 : How it is possible ?
Dattier   13
N 2 hours ago by Dattier
Source: les dattes à Dattier
Is it true that$$\forall n \in \mathbb N^*, (24^n \times B \mod A) \mod 2 = 0 $$?

A=1728400904217815186787639216753921417860004366580219212750904
024377969478249664644267971025952530803647043121025959018172048
336953969062151534282052863307398281681465366665810775710867856
720572225880311472925624694183944650261079955759251769111321319
421445397848518597584590900951222557860592579005088853698315463
815905425095325508106272375728975

B=2275643401548081847207782760491442295266487354750527085289354
965376765188468052271190172787064418854789322484305145310707614
546573398182642923893780527037224143380886260467760991228567577
953725945090125797351518670892779468968705801340068681556238850
340398780828104506916965606659768601942798676554332768254089685
307970609932846902
13 replies
Dattier
Mar 10, 2025
Dattier
2 hours ago
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Find min
hunghd8   8
N 2 hours ago by imnotgoodatmathsorry
Let $a,b,c$ be nonnegative real numbers such that $ a+b+c\geq 2+abc $. Find min
$$P=a^2+b^2+c^2.$$
8 replies
hunghd8
Yesterday at 12:10 PM
imnotgoodatmathsorry
2 hours ago
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Inequality and function
srnjbr   5
N 2 hours ago by pco
Find all f:R--R such that for all x,y, yf(x)+f(y)>=f(xy)
5 replies
srnjbr
Yesterday at 4:26 PM
pco
2 hours ago
J
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Difficult factorization
Dakernew192   1
N 2 hours ago by Thursday
x^5-2x+6
1 reply
Dakernew192
Jan 8, 2024
Thursday
2 hours ago
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every point is colored red or blue
Sayan   8
N 3 hours ago by Mathworld314
Source: ISI(BS) 2005 #9
Suppose that to every point of the plane a colour, either red or blue, is associated.

(a) Show that if there is no equilateral triangle with all vertices of the same colour then there must exist three points $A,B$ and $C$ of the same colour such that $B$ is the midpoint of $AC$.

(b) Show that there must be an equilateral triangle with all vertices of the same colour.
8 replies
Sayan
Jun 23, 2012
Mathworld314
3 hours ago
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Isogonal conjugates
drmzjoseph   4
N 3 hours 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
3 hours ago
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Combinatorics Geometry
Wasdshift   0
4 hours 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
4 hours ago
0 replies
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9 Three concurrent chords
v_Enhance   4
N 4 hours 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
4 hours ago
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Factoring Marathon
pican   1437
N 5 hours ago by aidan0626
Hello guys,
I think we should start a factoring marathon. Post your solutions like this SWhatever, and your problems like this PWhatever. Please make your own problems, and I'll start off simple: P1
1437 replies
pican
Aug 4, 2015
aidan0626
5 hours ago
J
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Confirming a number theoretical result
OlympusHero   1
N 6 hours ago by aidan0626
Prove that $a \cdot c^{-1}+b \cdot d^{-1} = (ad+bc) \cdot (cd)^{-1} \pmod n$ where $\gcd(c,n) = \gcd(d,n) = 1$.
1 reply
OlympusHero
6 hours ago
aidan0626
6 hours ago
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How to convert base numbers directly without using base 10
DSL13   13
N 6 hours ago by giratina3
I don't understand the topic of how you convert bases directly without going from base 10 to the base that I desire. How do I get from one base to another without the use of base 10?

I watched videos on it but I don't really get the idea.
13 replies
DSL13
Mar 11, 2021
giratina3
6 hours ago
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Combi counting
Caasi_Gnow   1
N Thursday at 7:27 PM by franklin2013
Find the number of different ways to arrange seven people around a circular meeting table if A and B must sit together and C and D cannot sit next to each other. (Note: the order for A and B might be A,B or B,A)
1 reply
Caasi_Gnow
Mar 20, 2025
franklin2013
Thursday at 7:27 PM
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Combi counting
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Reveal topic tags
combinatorics
counting
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Caasi_Gnow
41 posts
Caasi_Gnow
#1 h  Mar 20, 2025, 7:39 AM
Y by
Find the number of different ways to arrange seven people around a circular meeting table if A and B must sit together and C and D cannot sit next to each other. (Note: the order for A and B might be A,B or B,A)
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franklin2013
173 posts
franklin2013
#2 h  Thursday at 7:27 PM
Y by
I guess this is right???
Solution:
We do this question by complementary counting:
Total Number of ways to arrange 7 people in a circle with A and B sitting together. We do this by treating AB or BA as a single person, then multiply the result by 2: $6!\cdot 2=1440$.
Now, we count the number of ways there are to arrange the 7 people such that A and B sit together while C and D also sit together. This time, we treat AB/BA and CD/DC as singular people, then multiply the result by 4: $5!\cdot 4=480$.
So, our final answer is $1440-480=960$.
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