IMO 1977 LL FRG12

Origin: FRG

Problem

Let z be an integer > 1 and let M be the set of all numbers of the form zk = 1 + z + \cdot \cdot \cdot + zk, k = 0, 1, . . . . Determine the set T of divisors of at least one of the numbers zk from M.

Solution

According to part (a) of the previous problem we can conclude that T = {n \inN | (n, z) = 1}.