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

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

July 20, 2018

greatest common divisorSequencenumber theory

Problem Statement

Prove that for every positive integer

d > 1

and

m

the sequence

a_n=2^{2^n}+d

contains two terms

a_k

and

a_l

(

k \neq l

) such that their greatest common divisor is greater than

m

.
Proposed by T. Hakobyan