MathDB

Let

a_1,a_2,a_3,\ldots

be an infinite sequence of positive integers such that

a_{n+2m}

divides

a_{n}+a_{n+m}

for all positive integers

n

and

m.

Prove that this sequence is eventually periodic, i.e. there exist positive integers

N

and

d

such that

a_n=a_{n+d}

for all

n>N.

N7