IMO 2007 Shortlist N1

Find all pairs (k,n) of positive integers for which 7k − 3n divides k4 + n2 . (Austria)

imomathematicsolympiadshortlistnumber-theory

IMO 2007 Shortlist N1

Category: Number Theory

Problem

Find all pairs (k,n) of positive integers for which 7k − 3n divides k4

  • n2 . (Austria)