Problem Statement

Zsigmondy numbers n to a, b, are the greatest divisor of an - bn that is coprime to am - bm for all positive integers m < n.

Suppose we set a = 2 and b = 1. (Zs(n,2,1)) For each n, find the divisors of an - bn and return the largest that is coprime to all of am - bm, where m is each of the positive integers 1 to n - 1. When n = 4, 24 - 14 = 15. The divisors of 15 are 1, 3, 5, and 15. For m = 1, 2, 3 we get 2-1, 22-12, 23-13, or 1, 3, 7. The divisors of 15 that are coprime to each are 5 and 1, (1 is always included). The largest coprime divisor is 5, so Zs(4,2,1) = 5.

When n = 6, 26 - 16 = 63; its divisors are 1, 3, 7, 9, 21, 63. The largest divisor coprime to all of 1, 3, 7, 15, 31 is 1, (1 is always included), so Zs(6,2,1) = 1.

If a particular an - bn is prime, then Zs(n,a,b) will be equal to that prime. 25 - 15 = 31 so Zs(5,2,1) = 31.

Let's start with the solution: