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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
J
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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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Inspired by my own results
sqing   2
N an hour ago by cazanova19921
Source: Own
Let $ a,b,c\geq \frac{1}{2} . $ Prove that
$$ (a+1)(b+2)(c +1)-15 abc\leq \frac{15}{4}$$$$ (a+1)(b+3)(c +1)-21abc\leq \frac{21}{4}$$$$(a+2)(b+1)(c +2)-25a b c \leq \frac{25}{4}$$$$ (a+2)(b+3)(c +2)-35a b c \leq \frac{35}{2}$$$$ (a+3)(b+1)(c +3)-49a b c \leq \frac{49}{4}$$$$ (a+3)(b+2)(c +3)-49a b c \leq \frac{49}{2}$$
2 replies
sqing
3 hours ago
cazanova19921
an hour ago
J
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Line through incenter tangent to a circle
Kayak   32
N an hour ago by L13832
Source: Indian TST D1 P1
In an acute angled triangle $ABC$ with $AB < AC$, let $I$ denote the incenter and $M$ the midpoint of side $BC$. The line through $A$ perpendicular to $AI$ intersects the tangent from $M$ to the incircle (different from line $BC$) at a point $P$> Show that $AI$ is tangent to the circumcircle of triangle $MIP$.

Proposed by Tejaswi Navilarekallu
32 replies
Kayak
Jul 17, 2019
L13832
an hour ago
J
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D1015 : A strange EF for polynomials
Dattier   3
N an hour ago by Dattier
Source: les dattes à Dattier
Find all $P \in \mathbb R[x,y]$ with $P \not\in \mathbb R[x] \cup \mathbb R[y]$ and $\forall g,f$ homeomorphismes of $\mathbb R$, $P(f,g)$ is an homoemorphisme too.
3 replies
Dattier
Mar 16, 2025
Dattier
an hour ago
J
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Which is the top institutes for NDA coaching in Dehradun?
aniket78   1
N an hour ago by Pengu14
The top institutes for NDA coaching in Dehradun are known for their well-structured programs that help aspirants succeed in the National Defence Academy entrance exam. These institutes provide comprehensive training that covers all aspects of the NDA exam, including Mathematics, General Ability, and English. Along with academic coaching, they also offer specialized physical training to ensure candidates are physically fit for the selection process. The faculty in these institutes is highly experienced, providing personalized attention and expert guidance to students. Additionally, many institutes also focus on personality development and interview preparation, helping students perform well in the SSB interview
1 reply
1 viewing
aniket78
an hour ago
Pengu14
an hour ago
J
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Turkey EGMO TST 2017 P6
nimueh   4
N an hour ago by Nobitasolvesproblems1979
Source: Turkey EGMO TST 2017 P6
Find all pairs of prime numbers $(p,q)$, such that $\frac{(2p^2-1)^q+1}{p+q}$ and $\frac{(2q^2-1)^p+1}{p+q}$ are both integers.
4 replies
nimueh
Jun 1, 2017
Nobitasolvesproblems1979
an hour ago
J
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An inequality
JK1603JK   4
N an hour ago by Quantum-Phantom
Source: unknown
Let a,b,c>=0: ab+bc+ca=3 then maximize P=\frac{a^2b+b^2c+c^2a+9}{a+b+c}+\frac{abc}{2}.
4 replies
JK1603JK
Yesterday at 10:28 AM
Quantum-Phantom
an hour ago
J
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Inspired by Abelkonkurransen 2025
sqing   1
N an hour ago by kiyoras_2001
Source: Own
Let $ a,b,c $ be real numbers such that $ a^2+4b^2+16c^2= abc. $ Prove that $$\frac{1}{a}+\frac{1}{2b}+\frac{1}{4c}\geq -\frac{1}{16}$$Let $ a,b,c $ be real numbers such that $ 4a^2+9b^2+16c^2= abc. $ Prove that $$ \frac{1}{2a}+\frac{1}{3b}+\frac{1}{4c}\geq -\frac{1}{48}$$
1 reply
sqing
Yesterday at 1:06 PM
kiyoras_2001
an hour ago
J
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Inspired by Titu Andreescu
sqing   0
2 hours ago
Source: Own
Let $ a,b,c>0 $ and $ a+b+c\geq 3abc . $ Prove that
$$a^2+b^2+c^2+1\geq \frac{4}{3}(ab+bc+ca) $$
0 replies
1 viewing
sqing
2 hours ago
0 replies
J
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Geometry challenging question
srnjbr   0
2 hours ago
Given a triangle ABC. A1, B1 and C1 are the points of contact of the inner circumcircle of the triangle with the sides BC, AC and AB respectively. The point of contact of AA1 with B1C1 and the circumcircle are called L and Q respectively. M is the midpoint of B1C1. The point of intersection of lines BC and B1C1 is called T. P is the foot of the perpendicular drawn to AT from point L. Show that points A1, M, Q and P lie on a circle.
0 replies
srnjbr
2 hours ago
0 replies
J
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Plane normal to vector
RenheMiResembleRice   0
2 hours ago
Source: Bian Wei
Solve the attached
0 replies
RenheMiResembleRice
2 hours ago
0 replies
J
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Complex numbers should be easy
RenheMiResembleRice   1
N 3 hours ago by RenheMiResembleRice
Source: Wenjing Kong
I cant do the last part. :(
1 reply
RenheMiResembleRice
3 hours ago
RenheMiResembleRice
3 hours ago
J
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what the yap
KevinYang2.71   19
N 5 hours ago by MathLuis
Source: USAMO 2025/3
Alice the architect and Bob the builder play a game. First, Alice chooses two points $P$ and $Q$ in the plane and a subset $\mathcal{S}$ of the plane, which are announced to Bob. Next, Bob marks infinitely many points in the plane, designating each a city. He may not place two cities within distance at most one unit of each other, and no three cities he places may be collinear. Finally, roads are constructed between the cities as follows: for each pair $A,\,B$ of cities, they are connected with a road along the line segment $AB$ if and only if the following condition holds:
[center]For every city $C$ distinct from $A$ and $B$, there exists $R\in\mathcal{S}$ such[/center]
[center]that $\triangle PQR$ is directly similar to either $\triangle ABC$ or $\triangle BAC$.[/center]
Alice wins the game if (i) the resulting roads allow for travel between any pair of cities via a finite sequence of roads and (ii) no two roads cross. Otherwise, Bob wins. Determine, with proof, which player has a winning strategy.

Note: $\triangle UVW$ is directly similar to $\triangle XYZ$ if there exists a sequence of rotations, translations, and dilations sending $U$ to $X$, $V$ to $Y$, and $W$ to $Z$.
19 replies
1 viewing
KevinYang2.71
Yesterday at 12:00 PM
MathLuis
5 hours ago
J
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Prove a polynomial has a nonreal root
KevinYang2.71   33
N 6 hours ago by MathLuis
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.
33 replies
+1 w
KevinYang2.71
Yesterday at 12:00 PM
MathLuis
6 hours ago
J
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USAMO 2025 vs USAMO 2024 Difficulty
BennettHuang   9
N 6 hours ago by bachkieu
What did you guys think, which one was harder? Please only share if you genuinely tried both years.
9 replies
BennettHuang
Today at 1:07 AM
bachkieu
6 hours ago
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Does anyone see USAJMO on their portal
averageguy   3
N Mar 19, 2025 by MathRook7817
On my portal underneath "competition available to be taken" I see nothing there even though I'm supposed to take the USAJMO tomorrow. Does anyone else see USA(J)MO underneath there. Is it supposed to appear there only tomorrow.
3 replies
averageguy
Mar 19, 2025
MathRook7817
Mar 19, 2025
J
Does anyone see USAJMO on their portal
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Reveal topic tags
AMC
USA(J)MO
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averageguy
32 posts
averageguy
#1 h  Mar 19, 2025, 3:13 AM • 1 Y
Y by elasticwealth
On my portal underneath "competition available to be taken" I see nothing there even though I'm supposed to take the USAJMO tomorrow. Does anyone else see USA(J)MO underneath there. Is it supposed to appear there only tomorrow.
Z K Y
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Schintalpati
581 posts
Schintalpati
#2 h  Mar 19, 2025, 3:18 AM
Y by
I don't see anything either, so u should be good
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cdm
273 posts
cdm
#3 h  Mar 19, 2025, 4:35 AM
Y by
nothing for me either
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MathRook7817
615 posts
MathRook7817
#4 h  Mar 19, 2025, 4:41 AM
Y by
nothing for me cuz im not taking it lol
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