Find the 2000th hexagonal tile in which the differences between it and its 6 neighbors yield 3 primes.
Find the sum of the perimeters of all almost equilateral triangles with integral side lengths and area.
Find the maximum remainder when (p − 1)n + (p + 1)n is divided by p2 for prime p.
Count the number of ways a space 50 units long could be filled by tiles, homogeneously, measuring 2, 3 or 4 units long.
Fill an empty row with blocks, a minimum length of 50 units, until the size of the row exceeds 1,000,000 units. The blocks must be separated by at least one empty space.
Count the ways a row measuring fifty units in length could be filled with blocks three units long. The blocks must be separated by at least one empty space.
Count the number of ways a space 50 units long could be filled by tiles, heterogeneously, measuring 2, 3 or 4 units long.
Find how many Pythagorean triangles allow tiling with a perimeter < 100,000,000.
The prime factorisation of binomial coefficients
Powers With Trailing Digits