Existencial refinament on the search of integer solutions for the diophantine equation x3+y3+z3=nx^3+y^3+z^3=n

We propose a new algorithm, call Sam to determinate the existence of the solutions for the equation $x^3+y^3+z^3=n$ for a fixed value $n > 0$ unknowComment: 7 page

Cracking the problem with 33

Inspired by the Numberphile video "The uncracked problem with 33" by Tim Browning and Brady Haran, we investigate solutions to $x^3+y^3+z^3=k$ for a few small values of $k$. We find the first known solution for $k=33$.Comment: 6 pages, submitted. Further searches that are in progress will be reported elsewher