# A classic gem of number theory from Waclaw Sierpinski

In 1966, Waclaw Sierpinski (1882-1969) proved that there exist infinitely many integers k such that each of the numbers $N = k.2^{n}+1$ where n is a natural number, is composite. Three years later, Selfridge proved that the number $k=78557$ is such a number. Prove this last result of Selfridge by establishing that, in this case, N is always divisible by 3, 5, 7, 13, 19, 37 or 73.