A classic gem of number theory from Waclaw Sierpinski

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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.

Please get cracking !!

Nalin Pithwa

 

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