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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
1 viewing
jlacosta
Mar 2, 2025
0 replies
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A problem
jokehim   2
N 3 minutes ago by jokehim
Source: me
Let $a,b,c>0$ and prove $$\sqrt{\frac{a+b}{c}}+\sqrt{\frac{c+b}{a}}+\sqrt{\frac{a+c}{b}}\ge \frac{3\sqrt{6}}{2}\cdot\sqrt{\frac{3(a^3+b^3+c^3)}{(a+b+c)^3}+1}.$$
2 replies
1 viewing
jokehim
Mar 1, 2025
jokehim
3 minutes ago
J
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Another FE
GreekIdiot   2
N 24 minutes ago by Primeniyazidayi
Find all functions $f: \mathbb{R} \rightarrow \mathbb{R}$ satisfying $f(f(x)+y)=f(x^2-y)+2025f(x)y \: \forall \: x,y \in \mathbb{R}$, where $\mathbb{R}$ denotes the set of all real numbers.
2 replies
1 viewing
GreekIdiot
3 hours ago
Primeniyazidayi
24 minutes ago
J
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P(x)=2^n has an integer root
Sayan   8
N an hour ago by Mysteriouxxx
Source: Bulgarian MO 2003: P6
Determine all polynomials $P(x)$ with integer coefficients such that, for any positive integer $n$, the equation $P(x)=2^n$ has an integer root.
8 replies
Sayan
May 22, 2014
Mysteriouxxx
an hour ago
J
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Number of Solutions is 2
Miku3D   28
N an hour ago by lelouchvigeo
Source: 2021 APMO P1
Prove that for each real number $r>2$, there are exactly two or three positive real numbers $x$ satisfying the equation $x^2=r\lfloor x \rfloor$.
28 replies
Miku3D
Jun 9, 2021
lelouchvigeo
an hour ago
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No more topics!
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H
Equality case being all distinct reals?
navi_09220114   1
N Saturday at 2:00 PM by pingupignu
Source: Own. Malaysian IMO TST 2025 P7
Given a real polynomial $P(x)=a_{2024}x^{2024}+\cdots+a_1x+a_0$ with degree $2024$, such that for all positive reals $b_1, b_2,\cdots, b_{2025}$ with product $1$, then; $$P(b_1)+P(b_2)+\cdots +P(b_{2025})\ge 0$$Suppose there exist positive reals $c_1, c_2, \cdots, c_{2025}$ with product $1$, such that; $$P(c_1)+P(c_2)+ \cdots +P(c_{2025})=0$$Is it possible that the values $c_1, c_2, \cdots, c_{2025}$ are all distinct?

Proposed by Ivan Chan Kai Chin
1 reply
navi_09220114
Saturday at 1:04 PM
pingupignu
Saturday at 2:00 PM
J
Equality case being all distinct reals?
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Reveal topic tags
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Source: Own. Malaysian IMO TST 2025 P7
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navi_09220114
474 posts
navi_09220114
#1 h  Saturday at 1:04 PM
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Given a real polynomial $P(x)=a_{2024}x^{2024}+\cdots+a_1x+a_0$ with degree $2024$, such that for all positive reals $b_1, b_2,\cdots, b_{2025}$ with product $1$, then; $$P(b_1)+P(b_2)+\cdots +P(b_{2025})\ge 0$$Suppose there exist positive reals $c_1, c_2, \cdots, c_{2025}$ with product $1$, such that; $$P(c_1)+P(c_2)+ \cdots +P(c_{2025})=0$$Is it possible that the values $c_1, c_2, \cdots, c_{2025}$ are all distinct?

Proposed by Ivan Chan Kai Chin
This post has been edited 1 time. Last edited by navi_09220114, Saturday at 1:05 PM
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pingupignu
45 posts
pingupignu
#2 h  Saturday at 2:00 PM
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lol
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