MathDB

Multiples of p expressable as

Source: 2004 Korea Junior Math Olympiad

June 28, 2024

number theoryprime numbersmultiple

Problem Statement

For an arbitrary prime number

p

, show that there exists infinitely many multiples of

p

that can be expressed as the form

\frac{x^2+y+1}{x+y^2+1}

Where

x, y

are some positive integers.