Prove that every rational number is representable as $x^4+y^4-z^4-t^4$ with rational $x,y,z,t$.
Problem
Source: Russian TST 2017, Day 6 P2 (Groups A & B)
Tags: number theory, algebra, rational number
Source: Russian TST 2017, Day 6 P2 (Groups A & B)
Tags: number theory, algebra, rational number
Prove that every rational number is representable as $x^4+y^4-z^4-t^4$ with rational $x,y,z,t$.