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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!
[*]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
J
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Prove a polynomial has a nonreal root
KevinYang2.71   39
N a few seconds ago by yanling
Source: USAMO 2025/2
Let $n$ and $k$ be positive integers with $k<n$. Let $P(x)$ be a polynomial of degree $n$ with real coefficients, nonzero constant term, and no repeated roots. Suppose that for any real numbers $a_0,\,a_1,\,\ldots,\,a_k$ such that the polynomial $a_kx^k+\cdots+a_1x+a_0$ divides $P(x)$, the product $a_0a_1\cdots a_k$ is zero. Prove that $P(x)$ has a nonreal root.
39 replies
KevinYang2.71
Mar 20, 2025
yanling
a few seconds ago
J
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Red Mop Chances
imagien_bad   29
N 6 minutes ago by hellohannah
What are my chances of making red mop with a 35 on jmo?
29 replies
+3 w
imagien_bad
Yesterday at 8:27 PM
hellohannah
6 minutes ago
J
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USAMO Grading
AdityaDwivedi   0
31 minutes ago
Hello,

I was wondering how USAMO grading works. For one of my solutions, I kinda generalized a part of my solution cause I assumed that the reader would be able to follow but idk if it’ll drop my score from a 7 to a 5 or 6. So how much detail to I rlly need to include to get full points?
0 replies
AdityaDwivedi
31 minutes ago
0 replies
J
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A parabolic triangle-USAJMO Problem 4
BarbieRocks   74
N an hour ago by zuat.e
A triangle is called a parabolic triangle if its vertices lie on a parabola $y = x^2$. Prove that for every nonnegative integer $n$, there is an odd number $m$ and a parabolic triangle with vertices at three distinct points with integer coordinates with area $(2^nm)^2$.
74 replies
+1 w
BarbieRocks
Apr 29, 2010
zuat.e
an hour ago
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2x+1 is a perfect square but the following x+1 integers are not.
Sumgato   7
N an hour ago by Davut1102
Source: Spain Mathematical Olympiad 2018 P1
Find all positive integers $x$ such that $2x+1$ is a perfect square but none of the integers $2x+2, 2x+3, \ldots, 3x+2$ are perfect squares.
7 replies
1 viewing
Sumgato
Mar 17, 2018
Davut1102
an hour ago
J
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Prove that P1(x), P2(x) ,... Pn(x) = k has no root
truongphatt2668   2
N an hour ago by truongphatt2668
Let $n \in \mathbb{N}^*$ and $P_1(x),P_2(x), \ldots P_n(x) \in \mathbb{Z}[x]$ such that $\mathrm{deg} P_i = 2, \forall i = \overline{1,n}$. Prove that exists many $k \in \mathbb{N}$ such that every equation: $P_i(x) = k, \forall i = \overline{1,n}$ has no real roots
2 replies
truongphatt2668
Today at 2:26 AM
truongphatt2668
an hour ago
J
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Geo: incircle, escircle, isotomic conjugate
XAN4   1
N an hour ago by deraxenrovalo
Source: Own
For $\triangle{ABC}$, Its incircle $\odot I$ and $A-$escircle $\odot I_A$ are tangent to $BC$ at $D$ and $E$ respectively. $AI$ intersects line $BC$ at $J$. Line $AD$ intersects $\odot I$ at $F$, and line $AE$ intersects $\odot I_A$ at $G$. Line $FG$ intersects $BC$ at $H$. Prove that $BJ=CH$.
1 reply
XAN4
Mar 19, 2025
deraxenrovalo
an hour ago
J
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special sets
ChubbyTomato426   0
an hour ago
Let $n$ be a positive integer. A subset $\{a, b, c, d\} \subseteq \{1, 2, . . . , 4n\}$ with four distinct elements is special if there exists a rearrangement $(x, y, z, w)$ of $(a, b, c, d)$ such that $xy -zw = 1$. Prove that the set $\{1, 2, . . . , 4n \}$ cannot be partitioned into $n$ special disjoint sets.
0 replies
1 viewing
ChubbyTomato426
an hour ago
0 replies
J
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2, 4, 5-Nim
cjquines0   2
N an hour ago by Mathdreams
Source: Philippines MO 2016/4
Two players, \(A\) (first player) and \(B\), take alternate turns in playing a game using 2016 chips as follows: the player whose turn it is, must remove \(s\) chips from the remaining pile of chips, where \(s \in \{ 2,4,5 \}\). No one can skip a turn. The player who at some point is unable to make a move (cannot remove chips from the pile) loses the game. Who among the two players can force a win on this game?
2 replies
cjquines0
Jan 21, 2017
Mathdreams
an hour ago
J
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old and easy imo inequality
Valentin Vornicu   211
N an hour ago by Mathdreams
Source: IMO 2000, Problem 2, IMO Shortlist 2000, A1
Let $ a, b, c$ be positive real numbers so that $ abc = 1$. Prove that
\[ \left( a - 1 + \frac 1b \right) \left( b - 1 + \frac 1c \right) \left( c - 1 + \frac 1a \right) \leq 1. \]
211 replies
Valentin Vornicu
Oct 24, 2005
Mathdreams
an hour ago
J
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Number of sign change in cos ka
Rohit-2006   2
N 2 hours ago by Rohit-2006
Let $0\leq\alpha\leq\pi$. Denote by $V_n(\alpha)$ the number of changes of signs in the
sequence
$$1, cos \alpha, cos 2\alpha, . . . , cos n\alpha.$$Then prove that
$$\lim_{n\rightarrow\infty}\frac{V_n(\alpha)}{n}=\frac{\alpha}{\pi}$$.
2 replies
Rohit-2006
2 hours ago
Rohit-2006
2 hours ago
J
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Collinearity with orthocenter
liberator   178
N 2 hours ago by endless_abyss
Source: IMO 2013 Problem 4
Let $ABC$ be an acute triangle with orthocenter $H$, and let $W$ be a point on the side $BC$, lying strictly between $B$ and $C$. The points $M$ and $N$ are the feet of the altitudes from $B$ and $C$, respectively. Denote by $\omega_1$ is the circumcircle of $BWN$, and let $X$ be the point on $\omega_1$ such that $WX$ is a diameter of $\omega_1$. Analogously, denote by $\omega_2$ the circumcircle of triangle $CWM$, and let $Y$ be the point such that $WY$ is a diameter of $\omega_2$. Prove that $X,Y$ and $H$ are collinear.

Proposed by Warut Suksompong and Potcharapol Suteparuk, Thailand
178 replies
liberator
Jan 4, 2016
endless_abyss
2 hours ago
J
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Obsolete NT
GreekIdiot   1
N 2 hours ago by amapstob
Source: older isl
Find all $n \in \mathbb{N}$ greater than $1$, such that, if $gcd(a,b)=1$, then $a \equiv b \: mod \: n \iff ab \equiv 1 \: mod \: n$
1 reply
GreekIdiot
3 hours ago
amapstob
2 hours ago
J
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Nice problem
hanzo.ei   0
2 hours ago
Given two positive integers \( m, n \) satisfying \( m > n \) and their sum is an even number, consider the quadratic polynomial:

\[ P(x) = x^2 - (m^2 - m + 1)x + (m^2 - n^2 - m)(n^2 + 1). \]
Prove that all roots of \( P(x) \) are positive integers but are not perfect squares.
0 replies
hanzo.ei
2 hours ago
0 replies
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JMO winner cutoffs
dolphinday   2
N Friday at 5:49 PM by dolphinday
What are JMO winner cutoffs typically?
are they the same as top 24 on https://web.evanchen.cc/exams/posted-usamo-statistics.pdf
2 replies
dolphinday
Friday at 5:46 PM
dolphinday
Friday at 5:49 PM
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JMO winner cutoffs
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Reveal topic tags
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dolphinday
1318 posts
dolphinday
#1 h  Friday at 5:46 PM
Y by
What are JMO winner cutoffs typically?
are they the same as top 24 on https://web.evanchen.cc/exams/posted-usamo-statistics.pdf
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The post below has been deleted. Click to close.
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Danielzh
480 posts
Danielzh
#2 h  Friday at 5:47 PM • 1 Y
Y by dolphinday
They are usually top 60

@below same thing respectively
This post has been edited 1 time. Last edited by Danielzh, Friday at 5:50 PM
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dolphinday
1318 posts
dolphinday
#3 h  Friday at 5:49 PM
Y by
Wait they changed winner to honors and top winner to top honors or something is that different
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