IMO 2010 Shortlist N3

Find the smallest number n such that there exist polynomials f1, f2, ..., fn with rational coefficients satisfying x2 7 ...

imomathematicsolympiadshortlistnumber-theory

IMO 2010 Shortlist N3

Category: Number Theory

Problem

Find the smallest number n such that there exist polynomials f1, f2, ..., fn with rational coefficients satisfying x2 7 f1pxq2 f2pxq2  fnpxq2 . (Poland)