MathDB

x + py = n , x + y = p^2 , NT system

Source: Eotvos 1905 p1

September 6, 2024

number theorysystem of equationsDiophantine equationdiophantine

Problem Statement

For given positive integers

n

and

p

, find neaessary and sufficient conditions for the system of equations

x + py = n , \\ x + y = p^2

to have a solution

(x, y, z)

of positive integers. Prove also that there is at most one such solution.