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k a May Highlights and 2025 AoPS Online Class Information
jlacosta   0
Thursday at 11:16 PM
May is an exciting month! National MATHCOUNTS is the second week of May in Washington D.C. and our Founder, Richard Rusczyk will be presenting a seminar, Preparing Strong Math Students for College and Careers, on May 11th.

Are you interested in working towards MATHCOUNTS and don’t know where to start? We have you covered! If you have taken Prealgebra, then you are ready for MATHCOUNTS/AMC 8 Basics. Already aiming for State or National MATHCOUNTS and harder AMC 8 problems? Then our MATHCOUNTS/AMC 8 Advanced course is for you.

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[list][*]May 9th, 4:30pm PT/7:30pm ET, Casework 2: Overwhelming Evidence — A Text Adventure, a game where participants will work together to navigate the map, solve puzzles, and win! All are welcome.
[*]May 19th, 4:30pm PT/7:30pm ET, What's Next After Beast Academy?, designed for students finishing Beast Academy and ready for Prealgebra 1.
[*]May 20th, 4:00pm PT/7:00pm ET, Mathcamp 2025 Qualifying Quiz Part 1 Math Jam, Problems 1 to 4, join the Canada/USA Mathcamp staff for this exciting Math Jam, where they discuss solutions to Problems 1 to 4 of the 2025 Mathcamp Qualifying Quiz!
[*]May 21st, 4:00pm PT/7:00pm ET, Mathcamp 2025 Qualifying Quiz Part 2 Math Jam, Problems 5 and 6, Canada/USA Mathcamp staff will discuss solutions to Problems 5 and 6 of the 2025 Mathcamp Qualifying Quiz![/list]
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0 replies
jlacosta
Thursday at 11:16 PM
0 replies
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x(x - y) = 8y - 7 in NxN
parmenides51   4
N 8 minutes ago by Namisgood
Source: JBMO 2008 Shortlist N1
Find all the positive integers $x$ and $y$ that satisfy the equation $x(x - y) = 8y - 7$
4 replies
parmenides51
Oct 14, 2017
Namisgood
8 minutes ago
J
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IMO Genre Predictions
ohiorizzler1434   3
N 22 minutes ago by NicoN9
Everybody, with IMO upcoming, what are you predictions for the problem genres?


Personally I predict: predict
3 replies
ohiorizzler1434
42 minutes ago
NicoN9
22 minutes ago
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Insects walk
Giahuytls2326   0
26 minutes ago
Source: somewhere in the internet
A 100 × 100 chessboard is divided into unit squares. Each square has an arrow pointing up, down, left, or right. The board square is surrounded by a wall, except to the right of the top right corner square. An insect is placed in one of the squares.

Every second, the insect moves one unit in the direction of the arrow in its square. As the insect moves, the arrow of the square it just left rotates 90° clockwise.

If the specified movement cannot be performed, then the insect will not move for that second, but the arrow in the square it is standing on will still rotate. Is it possible that the insect never leaves the board?
0 replies
Giahuytls2326
26 minutes ago
0 replies
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Equal sum of digits
Fudicuehfosonrcjeong   0
an hour ago
Is it true that for any two positive integers a, b there exists a positive integer k such that s(ka)=s(kb), where s(n) is sum of digits in base 10?
0 replies
Fudicuehfosonrcjeong
an hour ago
0 replies
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All possible values of k
Ecrin_eren   2
N 2 hours ago by DAVROS


The roots of the polynomial
x³ - 2x² - 11x + k
are r₁, r₂, and r₃.

Given that
r₁ + 2r₂ + 3r₃ = 0,
what is the product of all possible values of k?

2 replies
Ecrin_eren
Yesterday at 8:42 AM
DAVROS
2 hours ago
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Floor and exact value
Ecrin_eren   3
N 3 hours ago by cowstalker
The exact value of a real number a is denoted by [a] and
the fractional value {a}.
For example; [3.7]= 3 and {3, 7} = 0.7
For a positive real number x,
Given the equality of [x]{x} = 2023, what can
[X^2]-[x]^2 be?
3 replies
Ecrin_eren
Yesterday at 5:54 PM
cowstalker
3 hours ago
J
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Calculating combinatorial numbers
lgx57   7
N 3 hours ago by anduran
Try to simplify this expression:

$$\sum_{i=1}^n \sum_{j=1}^i C_{n}^i C_{n}^j$$
7 replies
lgx57
Mar 30, 2025
anduran
3 hours ago
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Inequalities
sqing   0
4 hours ago
Let $ a,b,c\geq 0 ,a+b+c =4. $ Prove that
$$2a +ab +ab^2c \leq\frac{63+5\sqrt 5}{8}$$$$2a +ab^2 +abc \leq \frac{4(68+5\sqrt {10})}{27}$$$$ 2a +a^2b + a b^2c^3\leq \frac{4(50+11\sqrt {22})}{27}$$
0 replies
sqing
4 hours ago
0 replies
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Inequalities
toanrathay   0
4 hours ago
Let \( a, b, c > 0 \) such that $2(b^2 + bc + c^2) = 1 - 3a^2,$ prove that
\[ a + b + c + \frac{1}{a} + \frac{1}{b} + \frac{1}{c} \geq 10. \]


0 replies
toanrathay
4 hours ago
0 replies
J
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Find the functions
Ecrin_eren   7
N Today at 12:07 AM by jasperE3
"Find all differentiable functions f that satisfy the condition f(x) + f(y) = f((x + y) / (1 - xy)) for all x, y ∈ R, where xy ≠ 1."
7 replies
Ecrin_eren
Thursday at 8:58 PM
jasperE3
Today at 12:07 AM
J
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2025 CMIMC team p7, rephrased
scannose   12
N Yesterday at 11:36 PM by lpieleanu
In the expansion of $(x^2 + x + 1)^{2024}$, find the number of terms with coefficient divisible by $3$.
12 replies
scannose
Apr 18, 2025
lpieleanu
Yesterday at 11:36 PM
J
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Floor function
Ecrin_eren   1
N Yesterday at 9:38 PM by alexheinis

How many different reel value of a are there which satisfies the equation floor(a) [a-floor(a)]=2024a ?
1 reply
Ecrin_eren
Yesterday at 5:38 PM
alexheinis
Yesterday at 9:38 PM
J
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Maximum value
Ecrin_eren   3
N Yesterday at 6:27 PM by Royal_mhyasd
a,b,c are positive real numbers such that
(a+b)^2 (a+c)^2=16abc
What is the maximum value of a+b+c
3 replies
Ecrin_eren
Yesterday at 1:30 PM
Royal_mhyasd
Yesterday at 6:27 PM
J
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How many pairs
Ecrin_eren   1
N Yesterday at 5:26 PM by Ecrin_eren


Let n be a natural number and p be a prime number. How many different pairs (n, p) satisfy the equation:

p + 2^p + 3 = n^2 ?



1 reply
Ecrin_eren
Yesterday at 3:08 PM
Ecrin_eren
Yesterday at 5:26 PM
J
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J
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Quick Oly question
Alpaca31415   0
Apr 20, 2025
What is China second round? Just asking because I did a few questions and I'm wondering about the difficulty. Also, are there mohs ratings for non-IMO ISL questions?
0 replies
Alpaca31415
Apr 20, 2025
0 replies
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Quick Oly question
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difficulty
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Alpaca31415
12 posts
Alpaca31415
#1 h  Apr 20, 2025, 2:17 AM
Y by
What is China second round? Just asking because I did a few questions and I'm wondering about the difficulty. Also, are there mohs ratings for non-IMO ISL questions?
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