[math-fun] Generalized Fibonacci sequences and arithmetic progressions

Given a two-sided generalized Fibonacci sequence ...,n-m,m,n,m+n,... (with m,n in Z and not both zero), must there exist a two-sided arithmetic progression ...,a-d,a,a+d,... (with a,d in Z and d nonzero) that is disjoint from it? Jim Propp