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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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Inequalities from SXTX
sqing   7
N 11 minutes ago by sqing
T702. Let $ a,b,c>0 $ and $ a+2b+3c=\sqrt{13}. $ Prove that $$ \sqrt{a^2+1} +2\sqrt{b^2+1} +3\sqrt{c^2+1} \geq 7$$S
T703. Let $ a,b $ be real numbers such that $ a+b\neq 0. $. Find the minimum of $ a^2+b^2+(\frac{1-ab}{a+b} )^2.$
T704. Let $ a,b,c>0 $ and $ a+b+c=3. $ Prove that $$ \frac{a^2+7}{(c+a)(a+b)} + \frac{b^2+7}{(a+b)(b+c)} +\frac{c^2+7}{(b+c)(c+a)} \geq 6$$S
7 replies
1 viewing
sqing
Feb 18, 2025
sqing
11 minutes ago
J
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Cool problem
jkim0656   2
N 13 minutes ago by joeym2011
Hey AoPS!
I came across a problem recently and it goes like this:
Which is greater:
$$2 ^ {100!} $$or $$2^{100}!$$Soo... can u guys help? thx!
:yoda: and may the force be with u!
Notes: I don't exactly know where this problem came from, but if u find that u are the orig maker of this problem feel free to drop me a PM and ill add u to my post :)
2 replies
jkim0656
26 minutes ago
joeym2011
13 minutes ago
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help me at this pls i'm so confused
myname17042005   12
N 24 minutes ago by sqing
if a, b, c are real numbers and a, b, c >0, prove that
pls help meee
12 replies
+1 w
myname17042005
Jun 12, 2020
sqing
24 minutes ago
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Inequalities
nhathhuyyp5c   2
N 39 minutes ago by nhathhuyyp5c
Let $a,b,c$ be positive reals such that $a+b+c+2=abc$. Find the maximum value of $$\frac{a+1}{a^2+2}+\frac{b+1}{b^2+2}+\frac{c+1}{c^2+2}$$Given $n\ge 2$ non-zero reals $x_1,x_2,\cdots x_n$ such that their sum is $100$. Prove that there exists two numbers $x_i,x_j$ such that $\frac{1}{2}\le \left|\frac{x_i}{x_j}\right|\le 2$
2 replies
nhathhuyyp5c
Jan 10, 2025
nhathhuyyp5c
39 minutes ago
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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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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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