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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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Prove that |a|≥2ⁿ+1
Rohit-2006   0
4 minutes ago
$P\in\mathbb{Z}[x]$ has degree $n$ having $n$ real roots in $(0,1)$. Suppose $a$ is the leading coefficient of $P$. Show that, $$\mid a\mid\geq2^n+1$$
0 replies
Rohit-2006
4 minutes ago
0 replies
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Why is the old one deleted?
EeEeRUT   9
N 15 minutes ago by Jupiterballs
Source: EGMO 2025 P1
For a positive integer $N$, let $c_1 < c_2 < \cdots < c_m$ be all positive integers smaller than $N$ that are coprime to $N$. Find all $N \geqslant 3$ such that $$\gcd( N, c_i + c_{i+1}) \neq 1$$for all $1 \leqslant i \leqslant m-1$

Here $\gcd(a, b)$ is the largest positive integer that divides both $a$ and $b$. Integers $a$ and $b$ are coprime if $\gcd(a, b) = 1$.

Proposed by Paulius Aleknavičius, Lithuania
9 replies
EeEeRUT
Apr 16, 2025
Jupiterballs
15 minutes ago
J
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divisibility+factorial+exponent
britishprobe17   0
26 minutes ago
Source: KTOM Maret 2025
Determine all pairs of natural numbers $(m,n)$ that satisfy $2^{n!}+1|2^{m!}+19$
0 replies
britishprobe17
26 minutes ago
0 replies
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inequalities
pennypc123456789   4
N 41 minutes ago by KhuongTrang
If $a,b,c$ are positive real numbers, then
$$ \frac{a + b}{a + 7b + c} + \dfrac{b + c}{b + 7c + a}+\dfrac{c + a}{c + 7a + b} \geq \dfrac{2}{3}$$
we can generalize this problem
4 replies
pennypc123456789
Yesterday at 1:53 PM
KhuongTrang
41 minutes ago
J
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hexagon with angles, 3 main diagonals and other 6 diagonals, equal, regular?
parmenides51   0
Jul 30, 2019
Source: 2016 Oral Moscow Geometry Olympiad grades 8-9 p1
Angles are equal in a hexagon, three main diagonals are equal and the other six diagonals are also equal. Is it true that it has equal sides?
0 replies
parmenides51
Jul 30, 2019
0 replies
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hexagon with angles, 3 main diagonals and other 6 diagonals, equal, regular?
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Reveal topic tags
hexagon
angles
diagonals
equal segments
geometry
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Source: 2016 Oral Moscow Geometry Olympiad grades 8-9 p1
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parmenides51
30629 posts
parmenides51
#1 h  Jul 30, 2019, 6:36 AM • 2 Y
Y by Adventure10, Mango247
Angles are equal in a hexagon, three main diagonals are equal and the other six diagonals are also equal. Is it true that it has equal sides?
This post has been edited 2 times. Last edited by parmenides51, Jul 30, 2019, 6:41 AM
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