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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)!

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[list][*]April 3rd (Webinar), 4pm PT/7:00pm ET, Learning with AoPS: Perspectives from a Parent, Math Camp Instructor, and University Professor
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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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FE inequality from Iran
mojyla222   3
N 7 minutes ago by amir_ali
Source: Iran 2025 second round P5
Find all functions $f:\mathbb{R}^+ \to \mathbb{R}$ such that for all $x,y,z>0$
$$ 3(x^3+y^3+z^3)\geq f(x+y+z)\cdot f(xy+yz+xz) \geq (x+y+z)(xy+yz+xz). $$
3 replies
mojyla222
Apr 19, 2025
amir_ali
7 minutes ago
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binomial sum ratio
thewayofthe_dragon   2
N 14 minutes ago by P162008
Source: YT
Someone please evaluate this ratio inside the log for any given n(I feel the sum doesn't have any nice closed form).
2 replies
thewayofthe_dragon
Jun 16, 2024
P162008
14 minutes ago
J
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Maximum Area of a triangle formed by 3 Lines
Kunihiko_Chikaya   1
N 22 minutes ago by Mathzeus1024
Let $a>1.$ In the $xy-$ plane with the origin $O$, the line $y=2-ax$ intersects the lines $y=x$, and $y=ax$ at the points $A,\ B$, respectively. Find the maximum value of the area of $\triangle{OAB}.$
1 reply
Kunihiko_Chikaya
Sep 28, 2020
Mathzeus1024
22 minutes ago
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Ring out the Old Year and ring in the New.
Kunihiko_Chikaya   1
N 30 minutes ago by Mathzeus1024
Let $a,\ b,\ c$ be positive real numbers.

Prove that

$$\sqrt[3]{\left(\frac{a^{2022}-a}{b}+\frac{2021}{a^{\frac{a}{b}}}+1\right)\left(\frac{b^{2022}-b}{c}+\frac{2021}{b^{\frac{b}{c}}}+1\right)\left(\frac{c^{2022}-c}{a}+\frac{2021}{c^{\frac{c}{a}}}+1\right)}$$
$$\geq 2022.$$
Proposed by Kunihiko Chikaya/December 31, 2021
1 reply
Kunihiko_Chikaya
Dec 31, 2021
Mathzeus1024
30 minutes ago
J
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Rational solutions to r^r=s^s
kred9   0
Apr 6, 2025
Source: 2025 Utah Math Olympiad #6
Call a positive rational number $r$ a friendly number if there exists a positive rational number $s \neq r$ such that $r^r = s^s$. Find, with proof, the second smallest friendly number.
0 replies
kred9
Apr 6, 2025
0 replies
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Rational solutions to r^r=s^s
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Source: 2025 Utah Math Olympiad #6
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kred9
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kred9
#1 h  Apr 6, 2025, 12:07 AM
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Call a positive rational number $r$ a friendly number if there exists a positive rational number $s \neq r$ such that $r^r = s^s$. Find, with proof, the second smallest friendly number.
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