Question

I bet no one can do this. Find x, y, and z such that x³+y³+z³=k, for each k from 1 to 100

Answer 1

It is a well-known fact that for any natural number k, there are no non-zero integers x, y, and z that satisfy x^3 + y^3 + z^3 = k, unless k = 1 or k = 8. This is known as Fermat's Last Theorem.

However, for k = 1, we have the solution (x, y, z) = (1, 0, 0) and for k = 8, we have the solution (x, y, z) = (2, −1, 1)

It's important to note that this problem is a complex mathematical problem, which was solved only by Andrew Wiles in 1994 using advanced mathematical theories such as Iwasawa theory and Galois representations.