Math Notes

Square and Circle

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

Numbers whose reverse equals 9 times the original

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

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

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

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

10 Twos and Random Operators

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

Surprise!

Minimum number of participants who must have the same total score

OC692 from Crux Mathematicorum Vol. 50, No. 7

Midy’s Theorem

Two segments inside a square.

geometric-probability

Two probability problems involving rolling dice

OC693 from Crux Mathematicorum Vol. 50, No. 7

A Problem from Iranian Mathematical Olympiad 1995

Harker Math Invitational 2024 Team #15

Crux Problem 4859

OC638 from Crux Mathematicorum Vol. 49, No. 6

OC635 from Crux Mathematicorum Vol. 49, No. 5

OC634 from Crux Mathematicorum Vol. 49, No. 5

OC633 from Crux Mathematicorum Vol. 49, No. 5

complex-numbers

OC632 from Crux Mathematicorum Vol. 49, No. 5

geometric-inequality

OC631 from Crux Mathematicorum Vol. 49, No. 5

Diophante A2856

Crux Problem 4803