11

Part of 2013 Ukraine Team Selection Test

Problems(1)

infinite primes p divide 2^{2^n} + a

Source: Ukraine TST 2013 p11

Specified natural number

a

. Prove that there are an infinite number of prime numbers

p

such that for some natural

n

2^{2^n} + a

is divisible by

p

number theoryprimesDivisibility