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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 22nd (Webinar), 4:00pm PT/7:00pm ET, Competitive Programming at AoPS (USACO).[/list]
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0 replies
1 viewing
jlacosta
Apr 2, 2025
0 replies
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Olympiad
sasu1ke   2
N 17 minutes ago by epl1
IMAGE
2 replies
sasu1ke
an hour ago
epl1
17 minutes ago
J
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How to judge a number is prime or not?
mingzhehu   1
N 2 hours ago 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
2 hours ago
J
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Eazy equation clap
giangtruong13   0
Yesterday at 4:03 PM
Find all $x,y,z$ satisfy that: $$\frac{x}{y+z}=2x-1; \frac{y}{x+z}=3y-1;\frac{z}{x+y}=5x-1$$
0 replies
giangtruong13
Yesterday at 4:03 PM
0 replies
J
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inequality
revol_ufiaw   3
N Yesterday at 2:55 PM by MS_asdfgzxcvb
Prove that that for any real $x \ge 0$ and natural number $n$,
$$x^n (n+1)^{n+1} \le n^n (x+1)^{n+1}.$$
3 replies
revol_ufiaw
Yesterday at 2:05 PM
MS_asdfgzxcvb
Yesterday at 2:55 PM
J
No more topics!
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J
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ABxCDxEF= BCxDxFA, concurrent, cyclic (Oral Moscow Team MO 2002.10A4)
parmenides51   2
N Jan 14, 2021 by parmenides51
Convex hexagon $ABCDEF$ is inscribed in a circle. Prove that its diagonals $AD, BE$ and $CF$ meet at one point if and only if $AB \cdot CD \cdot EF = BC\cdot DE \cdot FA$.
2 replies
parmenides51
Nov 19, 2020
parmenides51
Jan 14, 2021
J
ABxCDxEF= BCxDxFA, concurrent, cyclic (Oral Moscow Team MO 2002.10A4)
G H J
Reveal topic tags
geometry
hexagon
concurrency
concurrent
Cyclic
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G H BBookmark kLocked kLocked NReply
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parmenides51
30629 posts
parmenides51
#1 h  Nov 19, 2020, 9:31 PM
Y by
Convex hexagon $ABCDEF$ is inscribed in a circle. Prove that its diagonals $AD, BE$ and $CF$ meet at one point if and only if $AB \cdot CD \cdot EF = BC\cdot DE \cdot FA$.
Z K Y
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jasperE3
11165 posts
jasperE3
#3 h  Nov 23, 2020, 6:09 AM
Y by
Bumping as no one has answered it yet.
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parmenides51
30629 posts
parmenides51
#4 h  Jan 14, 2021, 7:28 AM
Y by
solved here and the converse here

half problem , => was also 1997 UNSW S1 Australia (solved also here)
also was 2009 Balkan Mo Shortlist G2
This post has been edited 4 times. Last edited by parmenides51, Jan 15, 2021, 4:54 PM
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