> are there an infinite number of possible solutions to this problem? Unknown. From the article: 'A major result would be to prove the conjecture that k = x³

> are there an infinite number of possible solutions to this problem? Unknown. From the article: 'A major result would be to prove the conjecture that k = x³ + y³ + z³ has infinitely many solutions for every whole number k, except those k that have a remainder of 4 or 5 after being divided by 9.'