MathDB

x divides y^2+m

Source: Italy TST 2002

September 23, 2008

algebrapolynomialVietanumber theoryrelatively primenumber theory unsolved

Problem Statement

Prove that for any positive integer

m

there exist an infinite number of pairs of integers

(x,y)

such that

(\text{i})

x

and

y

are relatively prime;

(\text{ii})

x

divides

y^2+m;

(\text{iii})

y

divides

x^2+m.