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k a April Highlights and 2025 AoPS Online Class Information
jlacosta   0
Apr 2, 2025
Spring is in full swing and summer is right around the corner, what are your plans? At AoPS Online our schedule has new classes starting now through July, so be sure to keep your skills sharp and be prepared for the Fall school year! Check out the schedule of upcoming classes below.

WOOT early bird pricing is in effect, don’t miss out! If you took MathWOOT Level 2 last year, no worries, it is all new problems this year! Our Worldwide Online Olympiad Training program is for high school level competitors. AoPS designed these courses to help our top students get the deep focus they need to succeed in their specific competition goals. Check out the details at this link for all our WOOT programs in math, computer science, chemistry, and physics.

Looking for summer camps in math and language arts? Be sure to check out the video-based summer camps offered at the Virtual Campus that are 2- to 4-weeks in duration. 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)!

Be sure to mark your calendars for the following events:
[list][*]April 3rd (Webinar), 4pm PT/7:00pm ET, Learning with AoPS: Perspectives from a Parent, Math Camp Instructor, and University Professor
[*]April 8th (Math Jam), 4:30pm PT/7:30pm ET, 2025 MATHCOUNTS State Discussion
April 9th (Webinar), 4:00pm PT/7:00pm ET, Learn about Video-based Summer Camps at the Virtual Campus
[*]April 10th (Math Jam), 4:30pm PT/7:30pm ET, 2025 MathILy and MathILy-Er Math Jam: Multibackwards Numbers
[*]April 22nd (Webinar), 4:00pm PT/7:00pm ET, Competitive Programming at AoPS (USACO).[/list]
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0 replies
jlacosta
Apr 2, 2025
0 replies
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MOP Emails
hellohannah   6
N 4 minutes ago by ezpotd
So mop emails are probably coming tomorrow, feel free to discuss here. I'll probably post when I hear that they're out unless I'm asleep
6 replies
1 viewing
hellohannah
Today at 4:59 AM
ezpotd
4 minutes ago
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{MathILy, MathILy-Er} 2025 Decisions Thread
mysterynotfound   1
N 35 minutes ago by dragonborn56
Discuss your decisions here!
also share any relevant details about your decisions if you want
1 reply
mysterynotfound
Today at 3:35 AM
dragonborn56
35 minutes ago
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complex analysis
functiono   1
N 2 hours ago by Mathzeus1024
Source: exam
find the real number $a$ such that

$\oint_{|z-i|=1} \frac{dz}{z^2-z+a} =\pi$
1 reply
functiono
Jan 15, 2024
Mathzeus1024
2 hours ago
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Computational Calculus
Munmun5   0
2 hours ago
1. Consider the set of all continuous and infinitely differentiable functions $f$ with domain $[0,2025]$ satisfying $f(0)=0,f'(0)=0,f'(2025)=1$ and $f''$ is strictly increasing on $[0,2025]$ Compute smallest real M such that all functions in this set ,$f(2025)<M$ .
2. Polynomials $A(x)=ax^3+abx^2-4x-c,B(x)=bx^3+bcx^2-6x-a,C(x)=cx^3+cax^2-9x-b$ have local extrema at $b,c,a$ respectively. find $abc$ . Here $a,b,c$ are constants .
3. Let $R$ be the region in the complex plane enclosed by curve $$f(x)=e^{ix}+e^{2ix}+\frac{e^{3ix}}{3}$$for $0\leq x\leq 2\pi$. Compute perimeter of $R$ .
0 replies
Munmun5
2 hours ago
0 replies
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Why is this series not the Fourier series of some Riemann integrable function
tohill   0
4 hours ago
$\sum_{n=1}^{\infty}{\frac{\sin nx}{\sqrt{n}}}$ (0<x<2π)
0 replies
tohill
4 hours ago
0 replies
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2021 AMC 12A #25
franzliszt   27
N 5 hours ago by Magnetoninja
Source: 2021 AMC 12A #25
Let $d(n)$ denote the number of positive integers that divide $n$, including $1$ and $n$. For example, $d(1)=1,d(2)=2,$ and $d(12)=6$. (This function is known as the divisor function.) Let \[f(n)=\frac{d(n)}{\sqrt[3]{n}}.\]There is a unique positive integer $N$ such that $f(N)>f(n)$ for all positive integers $n\ne N$. What is the sum of the digits of $N?$

$\textbf{(A) }5 \qquad \textbf{(B) }6 \qquad \textbf{(C) }7 \qquad \textbf{(D) }8\qquad \textbf{(E) }9$
27 replies
franzliszt
Feb 5, 2021
Magnetoninja
5 hours ago
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Discuss the Stanford Math Tournament Here
Aaronjudgeisgoat   283
N Today at 5:09 AM by techb
I believe discussion is allowed after yesterday at midnight, correct?
If so, I will put tentative answers on this thread.
By the way, does anyone know the answer to Geometry Problem 5? I was wondering if I got that one right
Also, if you put answers, please put it in a hide tag

Answers for the Algebra Subject Test
Estimated Algebra Cutoffs
Answers for the Geometry Subject Test
Estimated Geo Cutoffs
Answers for the Discrete Subject Test
Estimated Cutoffs for Discrete
Answers for the Team Round
Guts Answers
283 replies
Aaronjudgeisgoat
Apr 14, 2025
techb
Today at 5:09 AM
J
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Converging product
mathkiddus   10
N Today at 4:30 AM by HacheB2031
Source: mathkiddus
Evaluate the infinite product, $$\prod_{n=1}^{\infty} \frac{7^n - n}{7^n + n}.$$
10 replies
mathkiddus
Apr 18, 2025
HacheB2031
Today at 4:30 AM
J
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Find the formula
JetFire008   4
N Today at 12:36 AM by HacheB2031
Find a formula in compact form for the general term of the sequence defined recursively by $x_1=1, x_n=x_{n-1}+n-1$ if $n$ is even.
4 replies
JetFire008
Yesterday at 12:23 PM
HacheB2031
Today at 12:36 AM
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$f\circ g +g\circ f=0\implies n$ even
al3abijo   4
N Yesterday at 10:37 PM by alexheinis
Let $n$ a positive integer . suppose that there exist two automorphisms $f,g$ of $\mathbb{R}^n$ such that $f\circ g +g\circ f=0$ .
Prove that $n$ is even.
4 replies
al3abijo
Yesterday at 9:05 PM
alexheinis
Yesterday at 10:37 PM
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2025 OMOUS Problem 6
enter16180   2
N Yesterday at 9:06 PM by loup blanc
Source: Open Mathematical Olympiad for University Students (OMOUS-2025)
Let $A=\left(a_{i j}\right)_{i, j=1}^{n} \in M_{n}(\mathbb{R})$ be a positive semi-definite matrix. Prove that the matrix $B=\left(b_{i j}\right)_{i, j=1}^{n} \text {, where }$ $b_{i j}=\arcsin \left(x^{i+j}\right) \cdot a_{i j}$, is also positive semi-definite for all $x \in(0,1)$.
2 replies
enter16180
Apr 18, 2025
loup blanc
Yesterday at 9:06 PM
J
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Sum of multinomial in sublinear time
programjames1   0
Yesterday at 7:45 PM
Source: Own
A frog begins at the origin, and makes a sequence of hops either two to the right, two up, or one to the right and one up, all with equal probability.

1. What is the probability the frog eventually lands on $(a, b)$?

2. Find an algorithm to compute this in sublinear time.
0 replies
programjames1
Yesterday at 7:45 PM
0 replies
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Find the answer
JetFire008   1
N Yesterday at 6:42 PM by Filipjack
Source: Putnam and Beyond
Find all pairs of real numbers $(a,b)$ such that $ a\lfloor bn \rfloor = b\lfloor an \rfloor$ for all positive integers $n$.
1 reply
JetFire008
Yesterday at 12:31 PM
Filipjack
Yesterday at 6:42 PM
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Pyramid packing in sphere
smartvong   2
N Yesterday at 4:23 PM by smartvong
Source: own
Let $A_1$ and $B$ be two points that are diametrically opposite to each other on a unit sphere. $n$ right square pyramids are fitted along the line segment $\overline{A_1B}$, such that the apex and altitude of each pyramid $i$, where $1\le i\le n$, are $A_i$ and $\overline{A_iA_{i+1}}$ respectively, and the points $A_1, A_2, \dots, A_n, A_{n+1}, B$ are collinear.

(a) Find the maximum total volume of $n$ pyramids, with altitudes of equal length, that can be fitted in the sphere, in terms of $n$.

(b) Find the maximum total volume of $n$ pyramids that can be fitted in the sphere, in terms of $n$.

(c) Find the maximum total volume of the pyramids that can be fitted in the sphere as $n$ tends to infinity.

Note: The altitudes of the pyramids are not necessarily equal in length for (b) and (c).
2 replies
smartvong
Apr 13, 2025
smartvong
Yesterday at 4:23 PM
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Correlation between USAMO and CMO qualification
rantaccountcs   7
N Apr 7, 2025 by elasticwealth
What is the correlation between cmo qualification and usamo qualification? What proportion of Canadian usamo qualifiers are cmo qualifiers and what proportion of cmo qualifiers are usamo qualifiers?
7 replies
rantaccountcs
Nov 2, 2023
elasticwealth
Apr 7, 2025
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Correlation between USAMO and CMO qualification
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rantaccountcs
156 posts
rantaccountcs
#1 h  Nov 2, 2023, 7:56 PM
Y by
What is the correlation between cmo qualification and usamo qualification? What proportion of Canadian usamo qualifiers are cmo qualifiers and what proportion of cmo qualifiers are usamo qualifiers?
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David_Kim_0202
384 posts
David_Kim_0202
#2 h  Nov 3, 2023, 3:47 AM
Y by
can usa people take canadian math competitions?
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mrtheory
4 posts
mrtheory
#3 h  Mar 30, 2025, 6:03 PM
Y by
David_Kim_0202 wrote:
can usa people take canadian math competitions?

yes
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BS2012
999 posts
BS2012
#4 h  Mar 30, 2025, 6:14 PM
Y by
mrtheory wrote:
David_Kim_0202 wrote:
can usa people take canadian math competitions?

yes

Really?
https://cms.math.ca/competitions/cmo/#CMOeligibility wrote:
In order to be an official participant, all competitors:

must be a Canadian Citizen or Permanent Resident of Canada (but not necessarily residing in Canada currently),

must not have formally enrolled at a university or any other equivalent post-secondary institution and must not yet have graduated from high school (or equivalent),

must be currently attending school full-time since the start of the current school year,

must be less than 20 years old as of June 30 of the year of the Competition.

Additionally, the CJMO requires that competitors must be in grade ten or earlier.
(https://cms.math.ca/competitions/cmo/#CMOeligibility)
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mrtheory
4 posts
mrtheory
#5 h  Apr 7, 2025, 3:12 AM
Y by
@BS2012 Oh my fault I might have mixed it up Canadians can participate in USA math competitions but like CMS stated USA students shouldn't be able to
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babyzombievillager
392 posts
babyzombievillager
#6 h  Apr 7, 2025, 3:32 AM
Y by
BS2012 wrote:
mrtheory wrote:
David_Kim_0202 wrote:
can usa people take canadian math competitions?

yes

Really?
https://cms.math.ca/competitions/cmo/#CMOeligibility wrote:
In order to be an official participant, all competitors:

must be a Canadian Citizen or Permanent Resident of Canada (but not necessarily residing in Canada currently),

must not have formally enrolled at a university or any other equivalent post-secondary institution and must not yet have graduated from high school (or equivalent),

must be currently attending school full-time since the start of the current school year,

must be less than 20 years old as of June 30 of the year of the Competition.

Additionally, the CJMO requires that competitors must be in grade ten or earlier.
(https://cms.math.ca/competitions/cmo/#CMOeligibility)

does anyone remember the jcoons post about Canadians competing in American olympiads lol
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BS2012
999 posts
BS2012
#7 h  Apr 7, 2025, 11:37 AM
Y by
babyzombievillager wrote:
...

does anyone remember the jcoons post about Canadians competing in American olympiads lol
bruh they can
americans cant participate in canadian olympiads but canadians can participate in american ones
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elasticwealth
317 posts
elasticwealth
#8 h  Apr 7, 2025, 11:42 AM
Y by
reasonable crash out imo
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