4

Part of 2018 Tuymaada Olympiad

Problems(1)

Greatest Common Divisor of Sequence 2^2^n+d

Source: Tuymaada 2018 Senior League/Problem 4, Junior League/Problem 4

Prove that for every positive integer

d > 1

m

a_n=2^{2^n}+d

contains two terms

a_k

a_l

k \neq l

) such that their greatest common divisor is greater than

m

.
Proposed by T. Hakobyan

greatest common divisorSequencenumber theory