Finding the maximum remainder when (a − 1)n + (a + 1)n is divided by a2.
Investigate the game of chance involving colored discs.
Find the maximum remainder when (p − 1)n + (p + 1)n is divided by p2 for prime p.
Find the kth element in a sorted list of radicals.
Finding square sums that are palindromic.
Find the 2000th hexagonal tile in which the differences between it and its 6 neighbors yield 3 primes.
Investigating minimal repunits that divide by n.
Finding composite values, n, for which n−1 is divisible by the length of the smallest repunits that divide it.
Determining the first forty prime factors of a very large repunit.
Investigating which primes will never divide a repunit containing 10**n digits.