Problem

Source: IMO Shortlist 1994, N4

Tags: number theory, IMO Shortlist, Sequence, recurrence relation



Define the sequences an,bn,cn as follows. a0=k,b0=4,c0=1. If an is even then an+1=an2, bn+1=2bn, cn+1=cn. If an is odd, then an+1=anbn2cn, bn+1=bn, cn+1=bn+cn. Find the number of positive integers k<1995 such that some an=0.