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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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Finally my algebra that I am proud of
mshtand1   1
N 14 minutes ago by RagvaloD
Source: Ukrainian Mathematical Olympiad 2025. Day 2, Problem 8.7
Find the smallest real number \(a\) such that for any positive integer number \(n > 2\) and any arrangement of the numbers from 1 to \(n\) on a circle, there exists a pair of adjacent numbers whose ratio (when dividing the larger number by the smaller one) is less than \(a\).

Proposed by Mykhailo Shtandenko
1 reply
mshtand1
Yesterday at 11:59 PM
RagvaloD
14 minutes ago
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f(2) = 7, find all integer functions [Taiwan 2014 Quizzes]
v_Enhance   54
N 39 minutes ago by Marcus_Zhang
Find all increasing functions $f$ from the nonnegative integers to the integers satisfying $f(2)=7$ and \[ f(mn) = f(m) + f(n) + f(m)f(n) \] for all nonnegative integers $m$ and $n$.
54 replies
v_Enhance
Jul 18, 2014
Marcus_Zhang
39 minutes ago
J
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Floor double summation
CyclicISLscelesTrapezoid   50
N an hour ago by Ilikeminecraft
Source: ISL 2021 A2
Which positive integers $n$ make the equation \[\sum_{i=1}^n \sum_{j=1}^n \left\lfloor \frac{ij}{n+1} \right\rfloor=\frac{n^2(n-1)}{4}\]true?
50 replies
CyclicISLscelesTrapezoid
Jul 12, 2022
Ilikeminecraft
an hour ago
J
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Binary expansion of sqrt3
v_Enhance   29
N an hour ago by Jack_w
Source: USA January TST for IMO 2016, Problem 1
Let $\sqrt 3 = 1.b_1b_2b_3 \dots _{(2)}$ be the binary representation of $\sqrt 3$. Prove that for any positive integer $n$, at least one of the digits $b_n$, $b_{n+1}$, $\dots$, $b_{2n}$ equals $1$.
29 replies
v_Enhance
May 17, 2016
Jack_w
an hour ago
J
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A great result
steven_zhang123   10
N Today at 9:35 AM by teomihai
Show that $\lim_{n \to \infty} \sum_{k=1}^{n} (\sqrt{1+\frac{k}{n^{2} } } -1)=\frac{1}{4} $.
10 replies
steven_zhang123
Oct 31, 2024
teomihai
Today at 9:35 AM
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Weird family of sequences
AndreiVila   9
N Today at 8:40 AM by Fibonacci_math
Source: Romanian District Olympiad 2025 12.3
[list=a]
[*] Let $a<b$ and $f:[a,b]\rightarrow\mathbb{R}$ be a strictly monotonous function such that $\int_a^b f(x) dx=0$. Show that $f(a)\cdot f(b)<0$.
[*] Find all convergent sequences $(a_n)_{n\geq 1}$ for which there exists a scrictly monotonous function $f:\mathbb{R}\rightarrow\mathbb{R}$ such that $$\int_{a_{n-1}}^{a_n} f(x)dx = \int_{a_n}^{a_{n+1}} f(x)dx,\text{ for all }n\geq 2.$$
9 replies
AndreiVila
Mar 8, 2025
Fibonacci_math
Today at 8:40 AM
J
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Monster Integral
Entrepreneur   1
N Today at 7:41 AM by RezerdPrime
$$\color{blue}{\int_{0}^{\pi} \frac{\tan^{-1}\left(\frac{\ln(\sin(x))}{x}\right)dx}{\ln^2\left(x^2 + \ln^2(\sin(x))\right) + 4\arctan^2\left(\frac{\ln(\sin(x))}{x}\right)}= -\frac{\pi \tan^{-1}\left(\frac{2\ln(2)}{\pi}\right)}{\ln^2\left(\frac{\pi^2}{4} + \ln^2(2)\right) + 4\arctan^2\left(\frac{2\ln(2)}{\pi}\right)}.}$$
1 reply
Entrepreneur
Jan 10, 2025
RezerdPrime
Today at 7:41 AM
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Integration Bee Kaizo
Calcul8er   41
N Today at 7:18 AM by Figaro
Hey integration fans. I decided to collate some of my favourite and most evil integrals I've written into one big integration bee problem set. I've been entering integration bees since 2017 and I've been really getting hands on with the writing side of things over the last couple of years. I hope you'll enjoy!
41 replies
Calcul8er
Mar 2, 2025
Figaro
Today at 7:18 AM
J
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convex closed set with a nonempty interior
ILOVEMYFAMILY   0
Today at 6:11 AM
a) When $n = 2$, prove that a convex closed set with a nonempty interior that contains exactly one extreme point must contain a ray. (SOLVED)

b) When $n = 2$, find all convex closed sets with a nonempty interior that contain exactly one extreme point.
0 replies
ILOVEMYFAMILY
Today at 6:11 AM
0 replies
J
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Differentiation Marathon!
LawofCosine   178
N Today at 5:26 AM by awzhang10
Hello, everybody!

This is a differentiation marathon. It is just like an ordinary marathon, where you can post problems and provide solutions to the problem posted by the previous user. You can only post differentiation problems (not including integration and differential equations) and please don't make it too hard!

Have fun!

(Sorry about the bad english)
178 replies
LawofCosine
Feb 1, 2025
awzhang10
Today at 5:26 AM
J
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Integrals problems and inequality
tkd23112006   1
N Today at 3:55 AM by removablesingularity
Let f be a continuous function on [0,1] such that f(x) ≥ 0 for all x ∈[0,1] and
$\int_x^1 f(t) dt \geq \frac{1-x^2}{2}$ , ∀x∈[0,1].
Prove that:
$\int_0^1 (f(x))^{2021} dx \geq \int_0^1 x^{2020} f(x) dx$
1 reply
tkd23112006
Feb 16, 2025
removablesingularity
Today at 3:55 AM
J
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Putnam 1972 B2
sqrtX   2
N Today at 1:17 AM by Tip_pay
Source: Putnam
A particle moves in a straight line with monotonically decreasing acceleration. It starts from rest and has velocity $v$ a distance $d$ from the start. What is the maximum time it could have taken to travel the distance $d$?
2 replies
sqrtX
Feb 17, 2022
Tip_pay
Today at 1:17 AM
J
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Putnam 1956 A3
sqrtX   2
N Today at 1:08 AM by Tip_pay
Source: Putnam 1956
A particle falls in a vertical plane from rest under the influence of gravity and a force perpendicular to and proportional to its velocity. Obtain the equations of the trajectory and identify the curve.
2 replies
sqrtX
Jul 1, 2022
Tip_pay
Today at 1:08 AM
J
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Certain amount of numbers t=x^3+y^2 in a given set
Tintarn   5
N Yesterday at 11:25 PM by Assassino9931
Source: VJIMC 2017, Category II, Problem 4
A positive integer $t$ is called a Jane's integer if $t = x^3+y^2$ for some positive integers $x$ and $y$. Prove
that for every integer $n \ge 2$ there exist infinitely many positive integers $m$ such that the set of $n^2$ consecutive
integers $\{m+1,m+2,\dotsc,m+n^2\}$ contains exactly $n + 1$ Jane's integers.
5 replies
Tintarn
Apr 2, 2017
Assassino9931
Yesterday at 11:25 PM
J
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J
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RMM 2024 shortlist problems
AbbyWong   1
N Today at 7:33 AM by AbbyWong
Hi everyone,
Could someone please send me the 2024 RMM Shortlist problems C1 and C2, if you have them?
1 reply
AbbyWong
Mar 7, 2025
AbbyWong
Today at 7:33 AM
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RMM 2024 shortlist problems
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Reveal topic tags
RMM Shortlist
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AbbyWong
#1 h  Mar 7, 2025, 11:09 AM
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Hi everyone,
Could someone please send me the 2024 RMM Shortlist problems C1 and C2, if you have them?
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AbbyWong
166 posts
AbbyWong
#2 h  Today at 7:33 AM
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