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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.

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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
jlacosta
Apr 2, 2025
0 replies
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Olympiad
sasu1ke   2
N 5 minutes ago by epl1
IMAGE
2 replies
sasu1ke
an hour ago
epl1
5 minutes ago
J
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How to judge a number is prime or not?
mingzhehu   1
N an hour 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
an hour ago
J
H
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!
H
J
H
only one angle >60^o , sides from ar. progreesion (2012 Kukin MO by OmSU 11.1.2)
parmenides51   3
N Apr 12, 2021 by natmath
The lengths of the sides of the triangle form an arithmetic progression with a nonzero difference. Prove that exactly one angle of this triangle is greater than $60$ degrees.

(Stern A.S.)
3 replies
parmenides51
Apr 12, 2021
natmath
Apr 12, 2021
J
only one angle >60^o , sides from ar. progreesion (2012 Kukin MO by OmSU 11.1.2)
G H J
Reveal topic tags
geometry
Arithmetic Progression
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parmenides51
30629 posts
parmenides51
#1 h  Apr 12, 2021, 4:04 AM
Y by
The lengths of the sides of the triangle form an arithmetic progression with a nonzero difference. Prove that exactly one angle of this triangle is greater than $60$ degrees.

(Stern A.S.)
This post has been edited 2 times. Last edited by parmenides51, Apr 12, 2021, 4:09 AM
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natmath
8219 posts
natmath
#2 h  Apr 12, 2021, 4:22 AM
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algebra, law of cosines bash
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ezpotd
1251 posts
ezpotd
#3 h  Apr 12, 2021, 4:55 AM
Y by
redacted i am high
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natmath
8219 posts
natmath
#4 h  Apr 12, 2021, 5:20 AM
Y by
@above, the sides are in arithmetic progression, not the angles...
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