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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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Turkey EGMO TST 2017 P6
nimueh   4
N 7 minutes ago by Nobitasolvesproblems1979
Source: Turkey EGMO TST 2017 P6
Find all pairs of prime numbers $(p,q)$, such that $\frac{(2p^2-1)^q+1}{p+q}$ and $\frac{(2q^2-1)^p+1}{p+q}$ are both integers.
4 replies
nimueh
Jun 1, 2017
Nobitasolvesproblems1979
7 minutes ago
J
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An inequality
JK1603JK   4
N 17 minutes ago by Quantum-Phantom
Source: unknown
Let a,b,c>=0: ab+bc+ca=3 then maximize P=\frac{a^2b+b^2c+c^2a+9}{a+b+c}+\frac{abc}{2}.
4 replies
JK1603JK
Yesterday at 10:28 AM
Quantum-Phantom
17 minutes ago
J
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Inspired by Abelkonkurransen 2025
sqing   1
N 20 minutes ago by kiyoras_2001
Source: Own
Let $ a,b,c $ be real numbers such that $ a^2+4b^2+16c^2= abc. $ Prove that $$\frac{1}{a}+\frac{1}{2b}+\frac{1}{4c}\geq -\frac{1}{16}$$Let $ a,b,c $ be real numbers such that $ 4a^2+9b^2+16c^2= abc. $ Prove that $$ \frac{1}{2a}+\frac{1}{3b}+\frac{1}{4c}\geq -\frac{1}{48}$$
1 reply
sqing
Yesterday at 1:06 PM
kiyoras_2001
20 minutes ago
J
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Inspired by Titu Andreescu
sqing   0
36 minutes ago
Source: Own
Let $ a,b,c>0 $ and $ a+b+c\geq 3abc . $ Prove that
$$a^2+b^2+c^2+1\geq \frac{4}{3}(ab+bc+ca) $$
0 replies
sqing
36 minutes ago
0 replies
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No more topics!
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Lots of bashing for a 7x7 table
oVlad   1
N Sep 24, 2024 by FarrukhKhayitboyev
Source: Romania JBMO TST 2024 Day 2 P1
The integers from 1 to 49 are written in a $7\times 7$ table, such that for any $k\in\{1,2,\ldots,7\}$ the product of the numbers in the $k$-th row equals the product of the numbers in the $(8-k)$-th row.
[list=a]
[*]Prove that there exists a row such that the sum of the numbers written on it is a prime number.
[*]Give an example of such a table.
[/list]
Cristi Săvescu
1 reply
oVlad
Jul 31, 2024
FarrukhKhayitboyev
Sep 24, 2024
J
Lots of bashing for a 7x7 table
G H J
Reveal topic tags
combinatorics
table
L
G H BBookmark kLocked kLocked NReply
Source: Romania JBMO TST 2024 Day 2 P1
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oVlad
1721 posts
oVlad
#1 h  Jul 31, 2024, 12:45 PM
Y by
The integers from 1 to 49 are written in a $7\times 7$ table, such that for any $k\in\{1,2,\ldots,7\}$ the product of the numbers in the $k$-th row equals the product of the numbers in the $(8-k)$-th row.
  1. Prove that there exists a row such that the sum of the numbers written on it is a prime number.
  2. Give an example of such a table.
Cristi Săvescu
Z K Y
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FarrukhKhayitboyev
10 posts
FarrukhKhayitboyev
#2 h  Sep 24, 2024, 1:45 PM
Y by
Observe that $29,31,37,41,43,47$ are primes that are over $49/2$ which means they all should be in one row($k=4$).
See that the last number on the $4$th row should be $13$ because numbers that $13$ divides in the set of number from $1$ to $49$ are $13,2*13,3*13$, we pick the number $13$ for the last spot because the product of all rows except $4$th should be a quadratic number. So the sum of the $4$th row is $241$ and $241$ is a prime number and we are done.
Example of such board is pretty simple to construct,so I will leave it to the reader.
This post has been edited 1 time. Last edited by FarrukhKhayitboyev, Sep 24, 2024, 1:48 PM
Reason: Corrected it, so there will be no confusion
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