Determine, with proof, all the integer solutions of the equation $x^3 + 2y^3 + 4z^3 - 6xyz = 1$.
Problem
Source: Indian Postal Coaching 2009 set 1 p2
Tags: diophantine, Diophantine equation, number theory
Source: Indian Postal Coaching 2009 set 1 p2
Tags: diophantine, Diophantine equation, number theory
Determine, with proof, all the integer solutions of the equation $x^3 + 2y^3 + 4z^3 - 6xyz = 1$.