Showing what's behind the curtain

Find the maximum remainder when (`p` − 1)^{n} + (`p` + 1)^{n} is divided by `p`^{2} for prime `p`.

Find the 2000th hexagonal tile in which the differences between it and its 6 neighbors yield 3 primes.

Find how many Pythagorean triangles allow tiling with a perimeter < 100,000,000.

The prime factorisation of binomial coefficients

Find the number of factors in an enormous factorial.

Find a minimum path sum in a matrix from the top left to the bottom right corners by moving up, down, left or right.

Find a set of terms that produce longest set of consecutive digits

Find the sum of the perimeters of all *almost equilateral triangles* with integral side lengths and area.

Find the smallest member of the longest amicable chain

Find the largest square number formed by pairs of encoded anagrams.