IMO 2016 Shortlist N3

Define P(n) = n2 + n + 1. For any positive integers a and b, the set {P(a),P(a + 1),P(a + 2),...,P(a + b)} is said to be...

imomathematicsolympiadshortlistnumber-theory

IMO 2016 Shortlist N3

Category: Number Theory

Problem

Define P(n) = n2

  • n + 1. For any positive integers a and b, the set {P(a),P(a + 1),P(a + 2),...,P(a + b)} is said to be fragrant if none of its elements is relatively prime to the product of the other elements. Determine the smallest size of a fragrant set.