MathDB

There're two positive inegers

a_1<a_2

. For every positive integer

n \geq 3

let

a_n

be the smallest integer that bigger than

a_{n-1}

and such that there's unique pair

1\leq i< j\leq n-1

such that this number equals to

a_i+a_j

. Given that there're finitely many even numbers in this sequence. Prove that sequence

\{a_{n+1}-a_n \}

is periodic starting from some element.

Problem Statement