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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)!

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[list][*]April 3rd (Webinar), 4pm PT/7:00pm ET, Learning with AoPS: Perspectives from a Parent, Math Camp Instructor, and University Professor
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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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Inequalities
nhathhuyyp5c   0
35 minutes ago
Prove that for all positive real numbers \( a, b, c \), the following inequality holds:

\[ \sqrt{a + b} + \sqrt{b + c} + \sqrt{c + a} \geq \frac{4(ab + bc + ca)}{\sqrt{(a + b)(b + c)(c + a)}} \]
0 replies
nhathhuyyp5c
35 minutes ago
0 replies
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Inequalities
hn111009   3
N 3 hours ago by James4623009
Let $a,b,c>0$ satisfied $a^2+b^2+c^2=9.$ Find the minimum of $$P=\dfrac{a}{bc}+\dfrac{2b}{ca}+\dfrac{5c}{ab}.$$
3 replies
hn111009
4 hours ago
James4623009
3 hours ago
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Olympiad
sasu1ke   3
N 4 hours ago by sasu1ke
IMAGE
3 replies
sasu1ke
5 hours ago
sasu1ke
4 hours ago
J
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How to judge a number is prime or not?
mingzhehu   1
N Yesterday at 11:14 PM by scrabbler94
A=（10X1+1）(10X+1），X1，X∈N+
B=（10 X1+3）（10X+7），X∈N，X1∈N
C=(10 X1+9)(10X+9), X∈N，X1∈N
D=(10 X1+1)(10X+3), X1∈N+，X∈N
E=（10 X1+7）(10X+9），X∈N，X1∈N
F=（10 X1+1）（10X+7），X1∈N+，X∈N
G=（10 X1+3）（10X+9），X∈N，X1∈N
H=（10 X1+1）10X+9），X1∈N+，X∈N
I=（10 X1+3）（10X+3），X1∈N，X∈N
J=( 10X1+7)(10X+7),X∈N，X1∈N

For any natural number P∈{P=10N+1，n∈N}，make P=A or B or C
If P can make the roots of function group(ABC) without any root group completely made up of integer, P will be a prime
For any natural number P∈{P=10N+3，n∈N}，make P=D or E
If P can make the roots of function group(DE) without any root group completely made up
of integer, P will be a prime
For any natural number P∈{P=10N+7，n∈N}，make P=F or G
If P can make the roots of function group(FG) without any root group completely made up
of integer, P will be a prime
For any natural number P∈{P=10N+9，n∈N}，make P=H or I or J
If P can make the roots of function group(GIJ) without any root group completely made up
of integer, P will be a prime
1 reply
mingzhehu
Yesterday at 2:45 PM
scrabbler94
Yesterday at 11:14 PM
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parallelogram wanted, AC_1=CC_1 (2021 AESC MSU Internet Olympiad 7.3)
parmenides51   0
Apr 9, 2021
Triangle $ABC$ is inscribed in a circle with center $O$. It's altitudes are $CC_1$ and $BB_1$ meet at point $H$. It is known that $AC_1=CC_1$. Prove that $OC_1HB_1$ is parallelogram.
0 replies
parmenides51
Apr 9, 2021
0 replies
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parallelogram wanted, AC_1=CC_1 (2021 AESC MSU Internet Olympiad 7.3)
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parmenides51
#1 h  Apr 9, 2021, 1:52 PM
Y by
Triangle $ABC$ is inscribed in a circle with center $O$. It's altitudes are $CC_1$ and $BB_1$ meet at point $H$. It is known that $AC_1=CC_1$. Prove that $OC_1HB_1$ is parallelogram.
This post has been edited 1 time. Last edited by parmenides51, Apr 9, 2021, 1:52 PM
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