MathDB

diophantine p^3 + pm + 2zm = m^2 + pz + z^2

Source: LCOMA Costa Rica National Olympiad, Final Round, 2015 3.4 day2

September 30, 2021

number theoryDiophantine equationdiophantine

Problem Statement

Find all triples

(p,M, z)

of integers, where

p

is prime,

m

is positive and

z

is negative, that satisfy the equation

p^3 + pm + 2zm = m^2 + pz + z^2