Notes

Square and Circle

geometry

trigonometry

\((a+c)(b+d) = 1\)

inequality

Numbers whose reverse equals 9 times the original

combinatorics

Expected value of \(|OH|^2\)

geometry

trigonometry

Smallest polynomial \(f\) s.t. \(72 | f(x)\) if \(x\) is an integer

number-theory

\(a^2 + b^2\) divided by \(a+b\)

inequality

\(x^3 = 1\) mod \(p\) => \((x+1)^p = x^p + 1\) mod \({p^3}\)

number-theory

10 Twos and Random Operators

E(2 □ 2 □ 2 □ 2 □ 2 □ 2 □ 2 □ 2 □ 2 □ 2)

ABMC

combinatorics

expected-value

Surprise!

number-theory

sequence

Minimum number of participants who must have the same total score

number-theory

combinatorics

OC692 from Crux Mathematicorum Vol. 50, No. 7

crux

number-theory

Midy’s Theorem

number-theory

Two segments inside a square.

geometric-probability

combinatorics

Two probability problems involving rolling dice

probability

state-space

OC693 from Crux Mathematicorum Vol. 50, No. 7

crux

geometry

A Problem from Iranian Mathematical Olympiad 1995

math-olympiad

algebra

Harker Math Invitational 2024 Team #15

polynomial

algebra

Crux Problem 4859

crux

geometry

OC638 from Crux Mathematicorum Vol. 49, No. 6

crux

algebra

floor-function

OC635 from Crux Mathematicorum Vol. 49, No. 5

crux

inequality

OC634 from Crux Mathematicorum Vol. 49, No. 5

crux

number-theory

OC633 from Crux Mathematicorum Vol. 49, No. 5

crux

complex-numbers

OC632 from Crux Mathematicorum Vol. 49, No. 5

crux

geometry

geometric-inequality

OC631 from Crux Mathematicorum Vol. 49, No. 5

crux

geometry

Diophante A2856

algebra

floor-function

diophante

Crux Problem 4803

crux

number-theory