## If a3+b3+c3=Na^3+b^3+c^3=N, then x3+y3+z3+t3=Nx^3+y^3+z^3+t^3 = N in infinitely many ways?

It is well-known that, a3+b3+c3=N for N=1,2 is solvable in the integers in infinitely many ways . However, it is an open question (but is conjectured) that if for general N it has a solution, then it must have infinitely many. I’d like to propose a variant, Conjecture: If a3+b3+c3=N, then x3+y3+z3+t3=N in infinitely many … Read more