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k a April Highlights and 2025 AoPS Online Class Information
jlacosta   0
Apr 2, 2025
Spring is in full swing and summer is right around the corner, what are your plans? At AoPS Online our schedule has new classes starting now through July, so be sure to keep your skills sharp and be prepared for the Fall school year! Check out the schedule of upcoming classes below.

WOOT early bird pricing is in effect, don’t miss out! If you took MathWOOT Level 2 last year, no worries, it is all new problems this year! Our Worldwide Online Olympiad Training program is for high school level competitors. AoPS designed these courses to help our top students get the deep focus they need to succeed in their specific competition goals. Check out the details at this link for all our WOOT programs in math, computer science, chemistry, and physics.

Looking for summer camps in math and language arts? Be sure to check out the video-based summer camps offered at the Virtual Campus that are 2- to 4-weeks in duration. There are middle and high school competition math camps as well as Math Beasts camps that review key topics coupled with fun explorations covering areas such as graph theory (Math Beasts Camp 6), cryptography (Math Beasts Camp 7-8), and topology (Math Beasts Camp 8-9)!

Be sure to mark your calendars for the following events:
[list][*]April 3rd (Webinar), 4pm PT/7:00pm ET, Learning with AoPS: Perspectives from a Parent, Math Camp Instructor, and University Professor
[*]April 8th (Math Jam), 4:30pm PT/7:30pm ET, 2025 MATHCOUNTS State Discussion
April 9th (Webinar), 4:00pm PT/7:00pm ET, Learn about Video-based Summer Camps at the Virtual Campus
[*]April 10th (Math Jam), 4:30pm PT/7:30pm ET, 2025 MathILy and MathILy-Er Math Jam: Multibackwards Numbers
[*]April 22nd (Webinar), 4:00pm PT/7:00pm ET, Competitive Programming at AoPS (USACO).[/list]
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0 replies
jlacosta
Apr 2, 2025
0 replies
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4 var inequality
sealight2107   1
N 24 minutes ago by sealight2107
Source: Own
Let $a,b,c,d$ be positive reals such that $a+b+c+d+\frac{1}{abcd} = 18$. Find the minimum and maximum value of $a,b,c,d$
1 reply
sealight2107
Wednesday at 2:40 PM
sealight2107
24 minutes ago
J
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Inspired by SXTX (4)2025 Q712
sqing   1
N 44 minutes ago by sqing
Source: Own
Let $ a ,b,c>0 $ and $ (a+b)^2+2(b+c)^2+(c+a)^2=12. $ Prove that$$ abc(a+b+c) \leq \frac{9}{5} $$Let $ a ,b,c>0 $ and $ 2(a+b)^2+ (b+c)^2+2(c+a)^2=12. $ Prove that$$ abc(a+b+c) \leq \frac{9}{8} $$
1 reply
sqing
Yesterday at 11:59 AM
sqing
44 minutes ago
J
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2^x+3^x = yx^2
truongphatt2668   4
N an hour ago by Jackson0423
Prove that the following equation has infinite integer solutions:
$$2^x+3^x = yx^2$$
4 replies
truongphatt2668
Apr 22, 2025
Jackson0423
an hour ago
J
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Operations on Pebbles
MarkBcc168   23
N an hour ago by quantam13
Source: ISL 2022 C6
Let $n$ be a positive integer. We start with $n$ piles of pebbles, each initially containing a single pebble. One can perform moves of the following form: choose two piles, take an equal number of pebbles from each pile and form a new pile out of these pebbles. Find (in terms of $n$) the smallest number of nonempty piles that one can obtain by performing a finite sequence of moves of this form.
23 replies
MarkBcc168
Jul 9, 2023
quantam13
an hour ago
J
No more topics!
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Sum of max of some sequences is sum of powers
Miquel-point   0
Apr 6, 2025
Source: Romanian IMO TST 1981, Day 3 P1
Consider the set $M$ of all sequences of integers $s=(s_1,\ldots,s_k)$ such that $0\leqslant s_i\leqslant n,\; i=1,2,\ldots,k$ and let $M(s)=\max\{s_1,\ldots,s_k\}$. Show that
\[\sum_{s\in A} M(s)=(n+1)^{k+1}-(1^k+2^k+\ldots +(n+1)^k).\]
Ioan Tomescu
0 replies
Miquel-point
Apr 6, 2025
0 replies
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Sum of max of some sequences is sum of powers
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Source: Romanian IMO TST 1981, Day 3 P1
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Miquel-point
476 posts
Miquel-point
#1 h  Apr 6, 2025, 6:33 PM • 1 Y
Y by PikaPika999
Consider the set $M$ of all sequences of integers $s=(s_1,\ldots,s_k)$ such that $0\leqslant s_i\leqslant n,\; i=1,2,\ldots,k$ and let $M(s)=\max\{s_1,\ldots,s_k\}$. Show that
\[\sum_{s\in A} M(s)=(n+1)^{k+1}-(1^k+2^k+\ldots +(n+1)^k).\]
Ioan Tomescu
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