Find the smallest integer n that makes 11 x 14^n + 1, a prime number, or, prove that it doesn't exist.

let us prove by induction

for n = 1 it is trivial and then for some n we assume that it is a prime

11 x 14^n + 1 gives prime. say P

now for n+1 the eq becomes

11 x 14x14^n + 1

11 x (13+1)14^n +1

11 x 13x14^n +1 +11 x 14^n +13 -13

13(P) + P - 13

14P -13

Posted by phi on 2005-06-21 09:11:13