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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
[*]MATHCOUNTS/AMC 8 Advanced
[*]AMC 10 Problem Series[/list]
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)!

Be sure to mark your calendars for the following upcoming events:
[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!
[*]June 9th, Monday, 7:30pm ET, Game Jam: Operation Shuffle!, Come join us to play our second round of Operation Shuffle! If you enjoy number sense, logic, and a healthy dose of luck, this is the game for you. No specific math background is required; all are welcome.[/list]
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0 replies
jlacosta
Jun 2, 2025
0 replies
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Integration tricky problem
Nithish_kumar   0
19 minutes ago
Solve integration with limits  0 to π  1/(1+tanx)+1/(1+cotx)dx  result is defined as k
N==K+i²+log10(k) +1/4k -sin(1.21×10^-5 k).
Then N yield a value close to following options
A.e(exponential)
B.π
C.c(speed of light)
0 replies
Nithish_kumar
19 minutes ago
0 replies
J
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Find sets of positive integers (a,b) such that there exists a positive integer c
kyotaro   0
39 minutes ago
Find sets of positive integers (a,b) such that there exists a positive integer c such that $$a^n+b^{n+9} =c (mod 13),\forall n\in \mathbb N^*$$and $0<a,b<13$.
0 replies
kyotaro
39 minutes ago
0 replies
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Polynomials
P162008   0
2 hours ago
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 $f(-1).$
0 replies
P162008
2 hours ago
0 replies
J
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[SHS Sipnayan 2023] Series of Drama F-E
Magdalo   8
N 4 hours ago by trangbui
Find the units digit of
\[\sum_{n=1}^{2025}n^5\]
8 replies
Magdalo
Jun 1, 2025
trangbui
4 hours ago
J
No more topics!
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angles in right triangle,<ABD=<ACD (2021 YuMSh Olympiad Finals 7.3)
parmenides51   1
N May 29, 2021 by rayfish
In a triangle $ABC$, the angle $A$ is right. Let $BM$ be the median of the triangle, $D$ the midpoint of $BM$. It turned out that $\angle ABD = \angle ACD$. And what are these angles equal to?
1 reply
parmenides51
May 28, 2021
rayfish
May 29, 2021
J
angles in right triangle,<ABD=<ACD (2021 YuMSh Olympiad Finals 7.3)
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Reveal topic tags
geometry
angles
right triangle
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parmenides51
30653 posts
parmenides51
#1 h  May 28, 2021, 10:51 PM
Y by
In a triangle $ABC$, the angle $A$ is right. Let $BM$ be the median of the triangle, $D$ the midpoint of $BM$. It turned out that $\angle ABD = \angle ACD$. And what are these angles equal to?
Z K Y
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rayfish
1121 posts
rayfish
#2 h  May 29, 2021, 8:38 PM
Y by
Solution
This post has been edited 1 time. Last edited by rayfish, May 29, 2021, 8:38 PM
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