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k a June Highlights and 2025 AoPS Online Class Information
jlacosta   0
Jun 2, 2025
Congratulations to all the mathletes who competed at National MATHCOUNTS! If you missed the exciting Countdown Round, you can watch the video at this link. Are you interested in training for MATHCOUNTS or AMC 10 contests? How would you like to train for these math competitions in half the time? We have accelerated sections which meet twice per week instead of once starting on July 8th (7:30pm ET). These sections fill quickly so enroll today!

[list][*]MATHCOUNTS/AMC 8 Basics
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For those interested in Olympiad level training in math, computer science, physics, and chemistry, be sure to enroll in our WOOT courses before August 19th to take advantage of early bird pricing!

Summer camps are starting this month at the Virtual Campus in math and language arts that are 2 - to 4 - weeks in duration. Spaces are still available - don’t miss your chance to have a transformative summer experience. 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][*]June 5th, Thursday, 7:30pm ET: Open Discussion with Ben Kornell and Andrew Sutherland, Art of Problem Solving's incoming CEO Ben Kornell and CPO Andrew Sutherland host an Ask Me Anything-style chat. Come ask your questions and get to know our incoming CEO & CPO!
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0 replies
jlacosta
Jun 2, 2025
0 replies
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Extended Wilson's?
NamelyOrange   2
N 21 minutes ago by rhydon516
Let $\mathbb{Z}^*_n$ be the set of positive integers less than $n$ relatively prime to it. Is there a nice pattern for $\left(\prod_{k\in \mathbb{Z}^*_n} k\right) \text{ mod }n$? I know from a Wilson's theorem-style argument that it's either $1$ or $-1$, but when is it which?
2 replies
NamelyOrange
4 hours ago
rhydon516
21 minutes ago
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Hockey Sticks and apple Pie
BadAtCompetitionMath21420   0
an hour ago
How many triples of three-digit palindromes have a sum that is also a three-digit palindromes?


This is a problem I plan on adding to my competition, but I'm unsure if PIE was correct to use in the solution:
solution
Please critique this as hard as possible because I'm really uncomfortable with counting, and this problem has to be perfect.
0 replies
BadAtCompetitionMath21420
an hour ago
0 replies
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Exponents and Logarithms
wpdnjs   1
N 2 hours ago by RedFireTruck
Suppose A and B are positive real numbers for which log base A of B = log base B of A. If neither A nor B is 1 and A does not equal B, find the value of AB.
1 reply
wpdnjs
4 hours ago
RedFireTruck
2 hours ago
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Polynomials
P162008   5
N 2 hours ago by RedFireTruck
P1. Find $p(0) + p(5)$ where $p$ is a monic polynomial of degree $4$ satisfying $p(r) = 2^r ; r = 1,2,3,4.$

P2. Find $p(1), p(-1)$ where $p$ is a polynomial of smallest degree possible satisfying $p(r) = \frac{1}{r^2 - 1}; r = 2,3,4,\cdots, 10.$

P3. Find $k$ and $p(0)$, if polynomial $p$ satisfies $x.p(x) + 1 = k\left(\prod_{i = 1}^{5} (x - i)\right).$

P4. Find $p(0)$ where $p$ is a polynomial of smallest degree satisfying $p(r) = \frac{1}{r}; r = 1,2,3,\cdots,10.$

P5. Find $p(0),p(6),k$ and $\alpha$ if polynomial $p$ satisfies $(x^2 - 6x).p(x) + 1 = k\left(\prod_{i=1}^{5} (x - i)\right)(x - \alpha).$

P6. If $f(x)$ is a polynomial of degree $50$ such that $f(x) = \frac{x}{x + 1}; x = 0,1,2,\cdots,50.$ Evaluate $f(-1).$
5 replies
P162008
Today at 12:17 AM
RedFireTruck
2 hours ago
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No more topics!
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Geometry books
T.Mousavidin   4
N Apr 30, 2025 by compoly2010
Hello, I wanted to ask if anybody knows some good books for geometry that has these topics in:
Desargues's Theorem, Projective geometry, 3D geometry,
4 replies
T.Mousavidin
Apr 29, 2025
compoly2010
Apr 30, 2025
J
Geometry books
G H J
Reveal topic tags
projective geometry
geometry
3D geometry
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T.Mousavidin
3 posts
T.Mousavidin
#1 h  Apr 29, 2025, 4:25 PM • 1 Y
Y by M.Roueintan
Hello, I wanted to ask if anybody knows some good books for geometry that has these topics in:
Desargues's Theorem, Projective geometry, 3D geometry,
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martianrunner
212 posts
martianrunner
#2 h  Apr 29, 2025, 6:26 PM
Y by
egmo is always a good pick if you are at that level
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VivaanKam
182 posts
VivaanKam
#3 h  Apr 29, 2025, 7:46 PM
Y by
I don't know If it contains those but the aops book Introduction To Geometry by Richard Rusczyk is pretty good.
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Shan3t
431 posts
Shan3t
#4 h  Apr 29, 2025, 11:06 PM
Y by
T.Mousavidin wrote:
Hello, I wanted to ask if anybody knows some good books for geometry that has these topics in:
Desargues's Theorem, Projective geometry, 3D geometry,

EGMO(Euclidean Geometry by Evan Chen) is a very good book, and i believe it has all of those topics :D(3D geo, and projective for sure, idk abt Desargue's Theorem tho...)
This post has been edited 1 time. Last edited by Shan3t, Apr 29, 2025, 11:07 PM
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compoly2010
14 posts
compoly2010
#5 h  Apr 30, 2025, 12:10 AM
Y by
Another alternative is Geometry Revisited (Coxeter), which in my opinion holds a terser take to your desires. In particular, it also covers stereographic and gnomonic projections.

Personally, however, I find EGMO covers your topics sufficiently for olympiad purposes.

Both, if I recall correctly, do not cover some more advanced techniques such as MMP, or LinPoP.
This post has been edited 1 time. Last edited by compoly2010, Apr 30, 2025, 1:06 AM
Reason: clarity
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