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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.

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[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
J
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a/b + b/a never integer ?
MTA_2024   3
N 3 hours ago by ohiorizzler1434
Let $a$ and $b$ be 2 distinct positive integers.
Can $\frac a b +\frac b a $ be in an integer. Prove why ?
3 replies
1 viewing
MTA_2024
Yesterday at 3:08 PM
ohiorizzler1434
3 hours ago
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2014 Community AIME / Marathon ... Algebra Medium #1 quartic
parmenides51   5
N Yesterday at 7:17 PM by CubeAlgo15
Let there be a quartic function $f(x)$ with maximums $(4,5)$ and $(5,5)$. If $f(0) = -195$, and $f(10)$ can be expressed as $-n$ where $n$ is a positive integer, find $n$.

proposed by joshualee2000
5 replies
parmenides51
Jan 21, 2024
CubeAlgo15
Yesterday at 7:17 PM
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Inequalities
sqing   4
N Yesterday at 5:52 PM by DAVROS
Let $ a, b\geq 0 $ and $ \frac {a^2+a+1}{b^2-b+1}+\frac {b^2+b+1}{a^2-a+1} \geq 3 $. Prove that
$$ a+b+a^2+b^2 \geq 28-6\sqrt{21}$$Let $ a, b\geq 0 $ and $ \frac {a^2+a+1}{b^2-b+1}+\frac {b^2+b+1}{a^2-a+1} \geq 4 $. Prove that
$$ a+b+a^2+b^2 \geq 10-4\sqrt 5$$Let $ a, b\geq 0 $ and $ \frac {a^2+a+1}{b^2-b+1}+\frac {b^2+b+1}{a^2-a+1} \geq 5 $. Prove that
$$ a+b+a^2+b^2 \geq \frac {2(26-5\sqrt{13})}{9} $$Let $ a, b\geq 0 $ and $\frac {a^2+a+1}{b^2-b+1}+\frac {b^2+b+1}{a^2-a+1}\geq 3+ \sqrt {5} $. Prove that
$$ a+b+a^2+b^2 \geq 2$$
4 replies
sqing
Mar 14, 2025
DAVROS
Yesterday at 5:52 PM
J
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interesting problem
sausagebun   1
N Yesterday at 4:05 PM by mathprodigy2011
Six points, labeled A, B, C, D, E, and F, are positioned consecutively on a straight line. Let G be a point not located on this line. The following distances are given: AC = 26, BD = 22, CE = 31, DF = 33, AF = 73, CG = 40, and DG = 30. Determine the area of triangle BGE.
I brute forced this with trig, was wondering if theres a more elegant way of doing this
1 reply
sausagebun
Yesterday at 3:21 PM
mathprodigy2011
Yesterday at 4:05 PM
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No more topics!
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PHP + Fibonacci
SomeonecoolLovesMaths   5
N Yesterday at 2:03 AM by OronSH
The Question

I have tried to search this problem both inside/outside AoPS but was unable to find a solution, specifically with the use of PHP in it. It would be really helpful if someone posted a solution to it.
5 replies
SomeonecoolLovesMaths
Saturday at 10:39 PM
OronSH
Yesterday at 2:03 AM
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PHP + Fibonacci
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Reveal topic tags
Php
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SomeonecoolLovesMaths
3131 posts
SomeonecoolLovesMaths
#1 h  Saturday at 10:39 PM
Y by
The Question

I have tried to search this problem both inside/outside AoPS but was unable to find a solution, specifically with the use of PHP in it. It would be really helpful if someone posted a solution to it.
Z K Y
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RoyalPrince
120 posts
RoyalPrince
#2 h  Saturday at 10:41 PM
Y by
  There exists a Fibonacci number \(F_{n}\) that ends with 2007 zeros. But I can't find what number it is if that's what you're looking for
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SomeonecoolLovesMaths
3131 posts
SomeonecoolLovesMaths
#3 h  Saturday at 10:43 PM
Y by
RoyalPrince wrote:
There exists a Fibonacci number \(F_{n}\) that ends with 2007 zeros. But I can't find what number it is if that's what you're looking for

No not really that. I am looking for a proof for the existence of such a number.
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SomeonecoolLovesMaths
3131 posts
SomeonecoolLovesMaths
#4 h  Saturday at 10:59 PM
Y by
I would also love it if you guys could help me with this.

Let $a_1, a_2, \ldots, a_{20}$ be distinct positive integers not exceeding $70$. Show that there is some $k$ so that $a_i - a_j = k$ for four different pairs $(i, j)$.
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mathprodigy2011
220 posts
mathprodigy2011
#5 h  Yesterday at 1:36 AM
Y by
SomeonecoolLovesMaths wrote:
The Question

I have tried to search this problem both inside/outside AoPS but was unable to find a solution, specifically with the use of PHP in it. It would be really helpful if someone posted a solution to it.

Click to reveal hidden text
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OronSH
1718 posts
OronSH
#6 h  Yesterday at 2:03 AM
Y by
For any $k$ the sequence $F_n\pmod k$ is periodic, since there are finitely many possible pairs $(F_n,F_{n+1})$ so eventually one will repeat. Additionally since $F_n,F_{n+1}$ uniquely determine $F_{n-1}$ the sequence is purely periodic. Since $F_0=F_2-F_1=0$ there is some other $n$ with $F_n\equiv 0\pmod k$. Then take $k=10^{2007}$
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