The sequence (pn)n∈N is defined by p1=2 and, for n≥2, pn is the largest prime factor of p1p2⋯pn−1+1. Show that pn≠5 for all n.
Source: Croatian MO 2004 2nd Grade P3
Tags: number theory
The sequence (pn)n∈N is defined by p1=2 and, for n≥2, pn is the largest prime factor of p1p2⋯pn−1+1. Show that pn≠5 for all n.