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k a April Highlights and 2025 AoPS Online Class Information

jlacosta 0

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

Squence problem

AlephG_64 1

Source: 2025 Finals Portuguese Math Olympiad P1

Francisco wrote a sequence of numbers starting with $25$ . From the fourth term of the sequence onwards, each term of the sequence is the average of the previous three. Given that the first six terms of the sequence are natural numbers and that the sixth number written was $8$ , what is the fifth term of the sequence?

1 reply

+1 w

AlephG_64

Yesterday at 1:19 PM

RagvaloD

23 minutes ago

sqrt(2) and sqrt(3) differ in at least 1000 digits

Stuttgarden 1

Source: Spain MO 2025 P3

We write the decimal expressions of $\sqrt{2}$ and $\sqrt{3}$ as $\sqrt{2}=1.a_1a_2a_3\dots\quad\quad\sqrt{3}=1.b_1b_2b_3\dots$ where each $a_i$ or $b_i$ is a digit between 0 and 9. Prove that there exist at least 1000 values of $i$ between $1$ and $10^{1000}$ such that $a_i\neq b_i$ .

1 reply

Stuttgarden

Mar 31, 2025

sami1618

28 minutes ago

50 points in plane

pohoatza 12

Source: JBMO 2007, Bulgaria, problem 3

Given are $50$ points in the plane, no three of them belonging to a same line. Each of these points is colored using one of four given colors. Prove that there is a color and at least $130$ scalene triangles with vertices of that color.

12 replies

pohoatza

Jun 28, 2007

de-Kirschbaum

31 minutes ago

beautiful functional equation problem

Medjl 6

Source: Netherlands TST for BxMO 2017 problem 2

Let define a function $f: \mathbb{N} \rightarrow \mathbb{Z}$ such that :
$i)$ $f(p)=1$ for all prime numbers $p$ .
$ii)$ $f(xy)=xf(y)+yf(x)$ for all positive integers $x,y$
find the smallest $n \geq 2016$ such that $f(n)=n$

6 replies

Medjl

Feb 1, 2018

Sadigly

44 minutes ago

College Math Topics in undergraduate and graduate studies

Topics in undergraduate and graduate studies

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k a April Highlights and 2025 AoPS Online Class Information

jlacosta 0

0 replies

jlacosta

Apr 2, 2025

0 replies

IMC 2010 - Problem 1

uglysolutions 9

Let $0 < a < b$ . Prove that
$\int_a^b (x^2+1)e^{-x^2} dx \geq e^{-a^2} - e^{-b^2}$ .

9 replies

uglysolutions

Jul 26, 2010

PikaPika999

5 minutes ago

abc=a+b+c in ring

Miquel-point 1

Source: RNMO SHL 2025, grade 12

In which finite rings can we find three (not necessarily distinct) nonzero elements so that their sum equals their product?

David-Andrei Anghel

1 reply

Miquel-point

4 hours ago

Filipjack

an hour ago

Putnam 2001 A2

ahaanomegas 18

For each $k$ , $\mathcal{C}_k$ is biased so that, when tossed, it has probability $\tfrac{1}{(2k+1)}$ of falling heads. If the $n$ coins are tossed, what is the probability that the number of heads is odd? Express the answer as a rational function $n$ .

18 replies

ahaanomegas

Feb 26, 2012

Rohit-2006

3 hours ago

Putnam 2000 B4

ahaanomegas 5

Let $f(x)$ be a continuous function such that $f(2x^2-1)=2xf(x)$ for all $x$ . Show that $f(x)=0$ for $-1\le x \le 1$ .

5 replies

ahaanomegas

Sep 6, 2011

ZeroAlephZeta

4 hours ago

Featured Content

Problem of the Day 2006 Serbia Team Selection Test

2006 Serbia Team Selection Test

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2006 Serbia Team Selection Test

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2006 Serbia Team Selection Test

$Problem 1$ The set S = {1,2,3,...,2006} is partitioned into two disjoint subsets A and B
such that:
(i) 13 ∈ A;
(ii) if a ∈ A, b ∈ B, a+b ∈ S, then a+b ∈ B;
(iii) if a ∈ A, b ∈ B, ab ∈ S, then ab ∈ A.
Determine the number of elements of A

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A ball moves endlessly on a circular billiard table. When it hits the edge it is reflected. Show that if it passes through a point on the table three times, then it passes through it infinitely many times.

parmenides51

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Find the number of ways that a positive integer $n$ can be represented as a sum of one or more consecutive positive integers.

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The Poincare plane is a half-plane bounded by a line $R$ . The lines are taken to be
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(2) the semicircles with center on $R$ .
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parmenides51

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Find all $10$ digit numbers $a_0a_1...a_9$ such that for each $k, a_k$ is the number of times that the digit $k$ appears in the number.

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k a April Highlights and 2025 AoPS Online Class Information

jlacosta 0

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jlacosta

Apr 2, 2025

0 replies

Introducing myself at AoPS, and what's your magic wand?

asuth_asuth 603

Hi!

I'm Andrew Sutherland. I'm the new Chief Product Officer at AoPS. As you may have read, Richard is retiring and Ben Kornell and I are working together to lead the company now. I'm leading all the software and digital stuff at AoPS. I just wanted to say hello and introduce myself! I'm really excited to be part of the special community that is AoPS.

Previously, I founded Quizlet as a 15-year-old high school student. I did Course 6 at MIT and then left to lead Quizlet full-time for a total of 14 years. I took a few years off and now I'm doing AoPS! I wrote more about all that on my blog: https://asuth.com/im-joining-aops

I have a question for all of you. If you could wave a magic wand, and change anything about AoPS, what would it be? All suggestions welcome! Thank you.

603 replies

asuth_asuth

Mar 30, 2025

Yihangzh

7 minutes ago

You have used a banned term. Please edit and resubmit.

MathWinner121 56

I have been writing a blog post and it says there is a banned term. I checked it over and nothing seems to be wrong, there is no foul language or anything. Why does it show this and am I able to access the list of banned AoPS words so I can submit the post on my blog?

56 replies

1 viewing

MathWinner121

Today at 1:11 AM

PikaPika999

11 minutes ago

Is there a way

thegreatbrain 27

I there a way to delete some of the topic in my topics?

27 replies

thegreatbrain

Yesterday at 6:06 PM

Craftybutterfly

an hour ago

How to delete my post easily?

whwlqkd 14

How to delete my post(trash) easily and fast?

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whwlqkd

Today at 3:04 PM

AlienGirl05

2 hours ago

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