MathDB
Show that there is an infinite number of primes p

Source: German TST 3, P2, 2009, Exam set by Gunther Vogel

July 18, 2009
inductionnumber theoryprime numbersnumber theory unsolved

Problem Statement

Let (an)n∈N \left(a_n \right)_{n \in \mathbb{N}} defined by a_1 \equal{} 1, and a_{n \plus{} 1} \equal{} a^4_n \minus{} a^3_n \plus{} 2a^2_n \plus{} 1 for n≥1. n \geq 1. Show that there is an infinite number of primes p p such that none of the an a_n is divisible by p. p.
Back to ProblemsView on AoPS