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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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Quadric function
soryn   2
N 2 minutes ago by soryn
If f(x)=ax^2+bx+c, a,b,c integers, |a|>=3, and M îs the set of integers x for which f(x) is a prime number and f has exactly one integer solution,prove that M has at most three elements.
2 replies
soryn
5 hours ago
soryn
2 minutes ago
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The old one is gone.
EeEeRUT   6
N 3 minutes ago by Jupiterballs
Source: EGMO 2025 P2
An infinite increasing sequence $a_1 < a_2 < a_3 < \cdots$ of positive integers is called central if for every positive integer $n$ , the arithmetic mean of the first $a_n$ terms of the sequence is equal to $a_n$.

Show that there exists an infinite sequence $b_1, b_2, b_3, \dots$ of positive integers such that for every central sequence $a_1, a_2, a_3, \dots, $ there are infinitely many positive integers $n$ with $a_n = b_n$.
6 replies
EeEeRUT
Apr 16, 2025
Jupiterballs
3 minutes ago
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Prime Numbers
TRcrescent27   6
N 5 minutes ago by Namisgood
Source: 2015 Turkey JBMO TST
Let $p,q$ be prime numbers such that their sum isn't divisible by $3$. Find the all $(p,q,r,n)$ positive integer quadruples satisfy:
$$p+q=r(p-q)^n$$
Proposed by Şahin Emrah
6 replies
1 viewing
TRcrescent27
Jun 22, 2016
Namisgood
5 minutes ago
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nice fe with non-linear function being the answer
jjkim0336   2
N 26 minutes ago by jjkim0336
Source: own
f:R+ -> R+

f(xf(y)+y) = y f(y^2 +x)
2 replies
jjkim0336
Apr 8, 2025
jjkim0336
26 minutes ago
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No more topics!
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min path, spider in regular octagonal prism of edge 2, with a cobweb of 3 m
parmenides51   0
May 3, 2021
Source: 2019 Izumrud Olympiad Emerald by UrFU - Ural Federal University 10 v1 p4
There is a regular octagonal prism, all edges of which are equal to $2$ m. A spider sits in the center of one of the side faces. It can move on the surface prisms until its $3$ m long cobweb ends. The spider wondered if there were on the bases of the prism, points to which it can reach with at least two different shortest paths, and at the same time spending all the cobweb. Help the spider count the number of such points.

original wording
0 replies
parmenides51
May 3, 2021
0 replies
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min path, spider in regular octagonal prism of edge 2, with a cobweb of 3 m
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Source: 2019 Izumrud Olympiad Emerald by UrFU - Ural Federal University 10 v1 p4
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parmenides51
30629 posts
parmenides51
#1 h  May 3, 2021, 8:26 PM
Y by
There is a regular octagonal prism, all edges of which are equal to $2$ m. A spider sits in the center of one of the side faces. It can move on the surface prisms until its $3$ m long cobweb ends. The spider wondered if there were on the bases of the prism, points to which it can reach with at least two different shortest paths, and at the same time spending all the cobweb. Help the spider count the number of such points.

original wording
This post has been edited 1 time. Last edited by parmenides51, May 3, 2021, 8:27 PM
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