The corresponding equation for cubes and higher powers has no solution at all:for any power n≥3, there are no positive integer triples x, y, and z such that xn+yn=zn. This is the famous Fermat's Last Theorem, which in future mightbe known as Wiles’s Theorem as it was finally proved in the 1990s by Sir Andrew Wiles. Even for the case of cubes,first solved by Euler, this is a very difficult problem. It is, however, relatively easy to show that the sum of two fourth powers is never a square(and so certainly not a fourth power). This is enough to reduce the problem to the case where nis a prime p(meaning that ifwe solved the problem for all prime exponents, the general result would follow at once), and indeed the problem was solved for so-called regular primes in the19th century. However, the full solution was only realized as a consequence of Wiles settling a deep question called the Shimura–Taniyama Conjecture.