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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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0511 x^3 - y^3 = 2005(x^2 - y^2) 5th edition Round 1 p1
parmenides51   2
N Feb 18, 2023 by reeh_haan
Find all pairs of positive integers $x, y$ such that $x^3 - y^3 = 2005(x^2 - y^2)$.
2 replies
parmenides51
May 6, 2021
reeh_haan
Feb 18, 2023
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pdf of old 7 versions of mathlinks contest (all problem sets from all rounds)
parmenides51   8
N Nov 14, 2021 by parmenides51
here is the 7 versions' pdf, a few have solutions

post collections created so far: (forum collection)

Mathtlinks 2020: day 1 pdf, day 2 pdf, post collection

7th edition (April - July 2008)
6th edition (October 2005 - January 2006)
5th edition (April - July 2005)
4th edition (October 2004 - January 2005)
3rd edition (March - June 2004)
2nd edition (September - December 2003)
1st edition (February - May 2003)

PS. Related post in HSO
8 replies
parmenides51
May 31, 2020
parmenides51
Nov 14, 2021
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I would like to know your opinions
Valentin Vornicu   4
N Oct 18, 2021 by NathanTien
I would like to know your opinions about the first set of problems ...
4 replies
Valentin Vornicu
Mar 9, 2003
NathanTien
Oct 18, 2021
J
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the opinions about the second set of problems
Valentin Vornicu   1
N May 14, 2021 by NathanTien
seemed to me that they were a little bit too easy :)
i think i have upgraded the level a little bit in the third round :)
1 reply
Valentin Vornicu
Mar 24, 2003
NathanTien
May 14, 2021
J
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0221 inequalities 2nd edition Round 2 p1
parmenides51   1
N May 10, 2021 by parmenides51
Given are six reals $a, b, c, x, y, z$ such that $(a + b + c)(x + y + z) = 3$ and $(a^2 + b^2 + c^2)(x^2 + y^2 + z^2) = 4$.
Prove that $ax + by + cz \ge 0$.
1 reply
parmenides51
May 10, 2021
parmenides51
May 10, 2021
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0733
Valentin Vornicu   7
N May 10, 2021 by parmenides51
Find the greatest positive real number $ k$ such that the inequality below holds for any positive real numbers $ a,b,c$:
\[ \frac ab + \frac bc + \frac ca - 3 \geq k \left( \frac a{b + c} + \frac b{c + a} + \frac c{a + b} - \frac 32 \right). \]
7 replies
Valentin Vornicu
May 12, 2008
parmenides51
May 10, 2021
J
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0241 functional 2nd edition Round 4 p1
parmenides51   1
N May 10, 2021 by parmenides51
The real polynomial $f \in R[X]$ has an odd degree and it is given that $f$ is co-prime with $g(x) = x^2 - x - 1$ and
$$f(x^2 - 1) = f(x)f(-x), \forall x \in R.$$Prove that $f$ has at least two complex non-real roots.
1 reply
parmenides51
May 10, 2021
parmenides51
May 10, 2021
J
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0233 number theory 2nd edition Round 3 p3
parmenides51   1
N May 10, 2021 by parmenides51
Prove that for every positive integer $m$ there exists a positive integer N such that $S(2^n) > m$ for every positive integer $n > N$, where by $S(x)$ we denote the sum of digits of a positive integer $x$.
1 reply
parmenides51
May 10, 2021
parmenides51
May 10, 2021
J
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0222 number theory 2nd edition Round 2 p2
parmenides51   1
N May 10, 2021 by parmenides51
Let $\{a_n\}_{n\ge 0}$ be a sequence of rational numbers given by $a_0 = a_1 = a_2 = a_3 = 1$ and for all $n \ge 4$ we have $a_{n-4}a_n = a_{n-3}a_{n-1} + a^2_{n-2}$. Prove that all the terms of the sequence are integers.
1 reply
parmenides51
May 10, 2021
parmenides51
May 10, 2021
J
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0273 combo geo 2nd edition Round 7 p3
parmenides51   0
May 10, 2021
A convex polygon $P$ can be partitioned into $27$ parallelograms. Prove that it can also be partitioned into $21$ parallelograms.
0 replies
parmenides51
May 10, 2021
0 replies
J
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J
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0463 tetahedron 4th edition Round 6 p3
parmenides51   1
N May 7, 2021 by parmenides51
If $n>2$ is an integer and $x_1, \ldots ,x_n$ are positive reals such that
\[ \frac 1{x_1} + \frac 1{x_2} + \cdots + \frac 1{x_n} = n \]then the following inequality takes place
\[ \frac{x_2^2+\cdots+x_n^2}{n-1}\cdot \frac {x_1^2+x_3^2+\cdots +x_n^2} {n-1} \cdots \frac{x_1^2+\cdots+x_{n-1}^2}{n-1}\geq \left(\frac{x_1^2+...+x_n^2}{n}\right)^{n-1}. \]
1 reply
parmenides51
May 7, 2021
parmenides51
May 7, 2021
J
0463 tetahedron 4th edition Round 6 p3
G H J
Reveal topic tags
inequalities
4th edition
algebra
L
G H BBookmark kLocked kLocked NReply
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parmenides51
30627 posts
parmenides51
#1 h  May 7, 2021, 10:44 PM
Y by
If $n>2$ is an integer and $x_1, \ldots ,x_n$ are positive reals such that
\[ \frac 1{x_1} + \frac 1{x_2} + \cdots + \frac 1{x_n} = n \]then the following inequality takes place
\[ \frac{x_2^2+\cdots+x_n^2}{n-1}\cdot \frac {x_1^2+x_3^2+\cdots +x_n^2} {n-1} \cdots \frac{x_1^2+\cdots+x_{n-1}^2}{n-1}\geq \left(\frac{x_1^2+...+x_n^2}{n}\right)^{n-1}. \]
Z K Y
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parmenides51
30627 posts
parmenides51
#2 h  May 7, 2021, 11:07 PM
Y by
discussed here
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