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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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inequality
revol_ufiaw   3
N an hour ago 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
2 hours ago
MS_asdfgzxcvb
an hour ago
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How to judge a number is prime or not?
mingzhehu   0
an hour ago
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
0 replies
1 viewing
mingzhehu
an hour ago
0 replies
J
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What is an isogonal conjugate and why is it useful?
EaZ_Shadow   6
N an hour ago by maxamc
What is an isogonal conjugate and why is it useful? People use them in Olympiad geometry proofs but I don’t understand why and what is the purpose, as it complicates me because of me not understanding it.
6 replies
EaZ_Shadow
Dec 28, 2024
maxamc
an hour ago
J
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Any nice way to do this?
NamelyOrange   3
N 2 hours ago by pooh123
Source: Taichung P.S.1 math program tryouts

How many ordered pairs $(a,b,c)\in\mathbb{N}^3$ are there such that $c=ab$ and $1\le a\le b\le c\le60$?
3 replies
NamelyOrange
Apr 2, 2025
pooh123
2 hours ago
J
No more topics!
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J
H
90^o wanted, <BYX=<AYC, BY/YC =2 BX/XA (2012 Math. Multiathlon Reggata J 1.2)
parmenides51   0
Mar 20, 2021
On the sides $AB$ and $BC$ of triangle $ABC$, there are points $X$ and $Y$, respectively, such that $\angle BYX = \angle AYC$ and $\frac{BY}{Y C} = \frac{2BX}{XA}$ . Prove that triangle $ABC$ is right-angled.
0 replies
parmenides51
Mar 20, 2021
0 replies
J
90^o wanted, <BYX=<AYC, BY/YC =2 BX/XA (2012 Math. Multiathlon Reggata J 1.2)
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ratio
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right triangle
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parmenides51
#1 h  Mar 20, 2021, 11:31 AM
Y by
On the sides $AB$ and $BC$ of triangle $ABC$, there are points $X$ and $Y$, respectively, such that $\angle BYX = \angle AYC$ and $\frac{BY}{Y C} = \frac{2BX}{XA}$ . Prove that triangle $ABC$ is right-angled.
This post has been edited 2 times. Last edited by parmenides51, Apr 6, 2021, 6:31 PM
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