2

Part of 1997 Baltic Way

Problems(1)

1/2(a_1+a_m) is also a member of sequence

Source: Baltic Way 1997

Given a sequence

a_1,a_2,a_3,\ldots

of positive integers in which every positive integer occurs exactly once. Prove that there exist integers

\ell

m,\ 1<\ell <m

a_1+a_m=2a_{\ell}

algebra proposedalgebra