IMO 2014 Shortlist N7
Let c ě 1 be an integer. Define a sequence of positive integers by a1 “ c and an1 “ a3 n ´ 4c ¨ a2 n 5c2 ¨ an c for all ...
Category: Number Theory
Problem
Let c ě 1 be an integer. Define a sequence of positive integers by a1 “ c and
an1 “ a3 n ´ 4c ¨ a2 n 5c2
¨ an ` c
for all n ě 1. Prove that for each integer n ě 2 there exists a prime number p dividing an but
none of the numbers a1,...,an´1.
(Austria)