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k a June Highlights and 2025 AoPS Online Class Information

jlacosta 0

Congratulations to all the mathletes who competed at National MATHCOUNTS! If you missed the exciting Countdown Round, you can watch the video at this link. Are you interested in training for MATHCOUNTS or AMC 10 contests? How would you like to train for these math competitions in half the time? We have accelerated sections which meet twice per week instead of once starting on July 8th (7:30pm ET). These sections fill quickly so enroll today!

[list][*]MATHCOUNTS/AMC 8 Basics
[*]MATHCOUNTS/AMC 8 Advanced
[*]AMC 10 Problem Series[/list]
For those interested in Olympiad level training in math, computer science, physics, and chemistry, be sure to enroll in our WOOT courses before August 19th to take advantage of early bird pricing!

Summer camps are starting this month at the Virtual Campus in math and language arts that are 2 - to 4 - weeks in duration. Spaces are still available - don’t miss your chance to have a transformative summer experience. 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 upcoming events:
[list][*]June 5th, Thursday, 7:30pm ET: Open Discussion with Ben Kornell and Andrew Sutherland, Art of Problem Solving's incoming CEO Ben Kornell and CPO Andrew Sutherland host an Ask Me Anything-style chat. Come ask your questions and get to know our incoming CEO & CPO!
[*]June 9th, Monday, 7:30pm ET, Game Jam: Operation Shuffle!, Come join us to play our second round of Operation Shuffle! If you enjoy number sense, logic, and a healthy dose of luck, this is the game for you. No specific math background is required; all are welcome.[/list]
Our full course list for upcoming classes is below:
All classes run 7:30pm-8:45pm ET/4:30pm - 5:45pm PT unless otherwise noted.

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0 replies

jlacosta

Jun 2, 2025

0 replies

Four variables inequality

TNKT 2

Source: Tran Ngoc Khuong Trang

Problem. Let $a,b,c,d\neq 0:\ a+b+c+d=0$ then prove that
$3\left(\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2}+\frac{1}{d^2}\right)\ge \frac{64}{a^2+b^2+c^2+d^2}+2\left(\frac{1}{ab}+\frac{1}{bc}+\frac{1}{cd}+\frac{1}{da}+\frac{1}{ca}+\frac{1}{bd}\right).$ When does equality hold?

2 replies

TNKT

Jun 17, 2025

nexu

11 minutes ago

Σ(x + 2y)(z + 2x + 3y) <= 3/2

parmenides51 10

Source: JBMO 2011 Shortlist A2

Let $x, y, z$ be positive real numbers. Prove that:
$\frac{x + 2y}{z + 2x + 3y}+\frac{y + 2z}{x + 2y + 3z}+\frac{z + 2x}{y + 2z + 3x} \le \frac{3}{2}$

10 replies

parmenides51

Oct 14, 2017

Golden_Verse

14 minutes ago

Algebra equation

Math.hunter 2

Solve for real x, y.
(x^2 + 1)(y^2 + 1) + 4(x - 1)(y - 1) = 0

2 replies

Math.hunter

an hour ago

OGMATH

21 minutes ago

JBMO Shortlist 2022 A2

Lukaluce 14

Source: JBMO Shortlist 2022

Let $x, y,$ and $z$ be positive real numbers such that $xy + yz + zx = 3$ . Prove that
$\frac{x + 3}{y + z} + \frac{y + 3}{z + x} + \frac{z + 3}{x + y} + 3 \ge 27 \cdot \frac{(\sqrt{x} + \sqrt{y} + \sqrt{z})^2}{(x + y + z)^3}.$
Proposed by Petar Filipovski, Macedonia

14 replies

Lukaluce

Jun 26, 2023

Golden_Verse

22 minutes ago

College Math Topics in undergraduate and graduate studies

Topics in undergraduate and graduate studies

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College Math Topics in undergraduate and graduate studies

Topics in undergraduate and graduate studies

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114,449 topics

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k a June Highlights and 2025 AoPS Online Class Information

jlacosta 0

0 replies

jlacosta

Jun 2, 2025

0 replies

Discontinuous linear map

ILOVEMYFAMILY 0

Find a discontinuous linear map $A$ from the space $l^\infty$ (the space of bounded sequences) to $\mathbb{R}$

0 replies

ILOVEMYFAMILY

2 minutes ago

0 replies

Integral

Martin.s 6

$\int_0^{\pi/6}\arcsin\Bigl(\sqrt{\cos(3\psi)\cos\psi}\Bigr)\,d\psi.$

6 replies

Martin.s

May 14, 2025

smartvong

an hour ago

Series of function

Tricky123 0

Q) show that the sequence of functions $f_n:=\frac{1+2sin^{2}nx}{\sqrt{n}}$ is uniformly converges on $\mathbb{R}$ .

How to make an easy progress.

0 replies

Tricky123

an hour ago

0 replies

UM Integral Bee 2025 Preliminary Round

smartvong 1

Source: University Malaya Integral Bee

Contest format:
- 3-hour written test.
- Credit given for showing working steps.
- Non-programmable calculators allowed.

1. $\int^1_0 \frac{\ln(1+x)}{1+x^2} \,dx$
2. $\int^{\infty}_{-\infty}e^{-x^2}e^{-\frac{1}{x^2}} \,dx$
3. $\int^2_0 x\sqrt{x^{\ln x}\sqrt[3]{x^{\ln^2x}\sqrt[4]{x^{\ln^3x}\cdots}}}\,dx$
4. $\int^{\infty}_{-\infty}\mathrm{sech}\left(2x - \frac{1}{2x - 1}\right)\,dx$
5. $\int^{\infty}_0 \frac{x^2}{\lfloor x\rfloor !}\,dx$
6. $\int^{\frac{\pi}{2}}_0 \frac{1}{\sqrt{\cos x (1 + \sin x)}}\,dx$
7. $\lim_{n \to \infty}\int^{\infty}_{-\infty}2n\sin(x^{2n})\,dx$
8. $\int^{\infty}_{-\infty} \frac{x^2}{x^4 + x^3 - x^2 - x + 1}\,dx$
9. Given that $\alpha_0 \in \mathbb{R}$ , evaluate $\lim_{n \to \infty}\left(\int^{\alpha_0}_0\int^{\alpha_1}_0\int^{\alpha_2}_0\cdots\int^{\alpha_{n-1}}_0\int^{\alpha_n}_0e^x\,dx\,d\alpha_n\,d\alpha_{n-1}\cdots\,d\alpha_2\,d\alpha_1\right)$ 10. $\lim_{x \to 0^+} \int \frac{2x}{\sqrt{1 - x^4}\arcsin^2(x)} - \frac{2\arcsin(x^2)}{\sqrt{1-x^2}\arcsin^3(x)}\,dx$
11. $\int^4_1 \left(1 - \frac{1}{x^2}\right)e^{\sqrt{x} + \frac{1}{\sqrt{x}}}\,dx$
12. $\int^{\frac{3}{4}}_{\frac{1}{4}} f(f(x))\,dx; \quad f(x) = \frac{4^x}{2 + 4^x}$
13. $\int^1_0\arcsin\left(\sqrt{\frac{2}{\pi}\arcsin\left(\sqrt{x}\right)}\right)\,dx$
14. $\int^e_1 x^{(x + x^x)} \left(\frac{1}{x} + \ln(x) + \ln^2(x)\right)\,dx$
15. $\int \frac{x^3 - 21x^2 - 63x - 189}{x^4 - 81}\,dx$
16. $\int^{\pi/2}_0 \frac{\frac{\sin(x) + 1}{\cos(x) + 2}}{\frac{\sin(x) - 3}{\cos(x) - 4}}\,dx$
17. $\sum^{2025}_{n = 0}\int^1_0\frac{1}{2(x + n + 1)\sqrt{(x + n)(x + n + 1)}}\,dx$
18. $\int^1_0 \frac{1}{\left\lfloor\frac{1}{x}\right\rfloor} \,dx$
19. $\int^1_0 (1-x^{25})^{1/20} - (1-x^{20})^{1/25} \,dx$
20. $\int \prod^{n - 1}_{k = 1}\sqrt{2x^2 - 2x^2\cos\left(\frac{2\pi k}{n}\right)}\,dx$

1 reply

smartvong

4 hours ago

techb

3 hours ago

Featured Content

Problem of the Day 2021 South East Mathematical Olympiad

2021 South East Mathematical Olympiad

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Problem of the Day 2021 South East Mathematical Olympiad

2021 South East Mathematical Olympiad

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2021 South East Mathematical Olympiad

To commemorate the $43rd$ anniversary of the restoration of mathematics competitions, a mathematics enthusiast
arranges the first $2021$ integers $1,2,\dots,2021$ into a sequence $\{a_n\}$ in a certain order, so that the sum of any consecutive $43$ items in the sequence is a multiple of $43$ .
(1) If the sequence of numbers is connected end to end into a circle, prove that the sum of any consecutive $43$ items on the circle is also a multiple of $43$ ;
(2) Determine the number of sequences $\{a_n\}$ that meets the conditions of the question.

Generals

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Contest of the Week 2023 Serbia JBMO TST

2023 Serbia JBMO TST

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Contest of the Week 2023 Serbia JBMO TST

2023 Serbia JBMO TST

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2023 Serbia JBMO TST

Given is an isosceles triangle $ABC$ with $CA=CB$ and angle bisector $BD$ , $D \in AC$ . The line through the center $O$ of $(ABC)$ , perpendicular to $BD$ , meets $BC$ at $E$ . The line through $E$ , parallel to $BD$ , meets $AC$ at $F$ . Prove that $CE=DF$ .

a_507_bc

view topic

Let $a, b, c \in [0;1]$ be reals such that $ab+bc+ca=1$ . Find the minimal and maximal value of $a^3+b^3+c^3$ .

a_507_bc

view topic

Find all triples $(k, m, n)$ of positive integers such that $m$ is a prime and:

(1) $kn$ is a perfect square;

(2) $\frac{k(k-1)}{2}+n$ is a fourth power of a prime;

(3) $k-m^2=p$ where $p$ is a prime;

(4) $\frac{n+2}{m^2}=p^4$ .

a_507_bc

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Site Support Tech support and questions about AoPS classes and materials

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Site Support Tech support and questions about AoPS classes and materials

Tech support and questions about AoPS classes and materials

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k a June Highlights and 2025 AoPS Online Class Information

jlacosta 0

0 replies

jlacosta

Jun 2, 2025

0 replies

Filter by unsolved

Suntafayato 1

Lots of posts have many good solutions.

How to filter posts that have never been solved by anyone? A sufficient condition: posts with zero replies.

1 reply

Suntafayato

Yesterday at 3:23 AM

aidan0626

Yesterday at 3:28 AM

k error in contest collection

heheman 2

hello friends,
in the 2023 Iran MO 3rd round contest collection, the geometry section has been mistakenly titled as Algebra. Can someone fix?
Link:
https://artofproblemsolving.com/community/c3509728_2023_iran_mo_3rd_round
Screenshot provided as attachment

2 replies

heheman

Jun 18, 2025

jlacosta

Friday at 10:54 PM

k Long time to load

SI113 1

Not a complaint or anything, since it only takes max a minute, but is there any particular reason the AoPS wiki takes a while to load compared to other parts of the website?

1 reply

SI113

Friday at 10:27 PM

jlacosta

Friday at 10:29 PM

k Absolute Value

Yash1212 1

Does anybody know how to write the absolute value symbol in AoPS

1 reply

Yash1212

Jun 20, 2025

Demetri

Jun 20, 2025

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Contests in the 2024-25 school year

2025 239 Open Mathematical Olympiad
239 Open Mathematical Olympiad 2025

2025 Abelkonkurransen Finale
Norwegian MO 2025

2025 AIME
AIME 2025

2025 All-Russian Olympiad
All-Russian Olympiad 2025

2025 All-Russian Olympiad Regional Round
All-Russian Olympiad Regional Round 2025

2025 Austrian MO National Competition
Austrian MO National Competition 2025

2025 Austrian MO Regional Competition
Austrian MO Regional Competition 2025

2025 Azerbaijan Junior NMO
For junior (8-9 grades)

2025 Azerbaijan Senior NMO
For seniors (10-11 grades)

2025 Balkan MO
Balkan MO 2025

2025 Bangladesh Mathematical Olympiad
BdMO 2025 National Round Problems

2025 Belarusian National Olympiad
Belarusian National Olympiad 2025

2025 Benelux
2025 Benelux Mathematical Olympiad

2025 Bulgarian Spring Mathematical Competition
Bulgarian Spring Mathematical Competition 2025

2025 Bulgarian Winter Tournament
Bulgarian Winter Tournament 2025

2025 Bundeswettbewerb Mathematik
Bundeswettbewerb Mathematik 2025

2025 Canada Junior National Olympiad
Canada Junior National Olympiad 2025

2025 Canada National Olympiad
Canada National Olympiad 2025

2025 Caucasus Mathematical Olympiad
X Caucasus Mathematical Olympiad

2025 China National Olympiad
2025 China National Olympiad

2025 China Team Selection Test
China Team Selection Test 2025

2025 EGMO
European Girls MO 2025

2025 Euler Olympiad

2025 Francophone Mathematical Olympiad
Math olympiad for the French Speaking, 2025

2025 Greece National Olympiad
2025 Greece National Olympiad

2025 India National Olympiad
India National Olympiad 2025

2025 India STEMS

2025 International Zhautykov Olympiad
International Zhautykov Olympiad 2025

2025 Iran MO (2nd Round)
National Math Olympiad (Second Round) 2025

2025 Israel National Olympiad (Gillis)
An Olympiad for grades 7-12.

2025 Israel TST

2025 Japan MO Finals
Japan MO Finals 2025

2025 Korea - Final Round
FKMO 2025

2025 Korea Winter Program Practice Test
Korea Winter Program Practice Test 2025

2025 Kyiv City MO Round 1
Problems from first round of Kyiv Mathematical Olympiad 2025

2025 Kyiv City MO Round 2
Problems from second round of Kyiv Mathematical Olympiad 2025

2025 Macedonian Mathematical Olympiad
The problems from the 32nd Macedonian Mathematical Olympiad

2025 Macedonian TST
The problems from the 2025 Macedonian TST

2025 Malaysian APMO Camp Selection Test
Malaysian APMO Camp Selection Test for APMO 2025

2025 Nordic
Nordic 2025

2025 Philippine MO

2025 Poland - First Round

2025 Poland - Second Round
Second Round - Poland 2025

2025 Polish MO Finals
Polish MO Finals 2025

2025 Portugal MO
Portugal MO 2025

2025 Romanian Master of Mathematics
15th RMM 2025

2025 Sharygin Geometry Olympiad
Sharygin Geometry Olympiad 2025

2025 Spain Mathematical Olympiad
Spain Mathematical Olympiad 2025

2025 Taiwan TST Round 1

2025 Taiwan TST Round 2
Taiwan TST Round 2 2025

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