IMO 2011 Shortlist N7

Let p be an odd prime number. For every integer a, define the number Sa = a + a2 + ··· + ap−1 p − 1 . Let m and n be int...

imomathematicsolympiadshortlistnumber-theory

IMO 2011 Shortlist N7

Category: Number Theory

Problem

Let p be an odd prime number. For every integer a, define the number Sa = a + a2

  • ··· + ap−1 p − 1 . Let m and n be integers such that S3 + S4 − 3S2 = m n . Prove that p divides m.