Find a combination of three *different *positive integers *x*, *y*, and *z* such that:

*x*^{3} + *y*^{3} = *z*^{4}

Hint: there’s a better way than brute force / trial & error.

#### Solution

There are infinitely many solutions, so here’s a key insight to easily find one:

It’s trivial to find some three different positive integers a, b, and c such that:

*a*^{3} + *b*^{3} = *z*

Then multiple both sides by *z*^{3}:

(*az*)^{3} + (*bz*)^{3} = *z*^{4}

Let *x* = *az*, *y* = *bz*, and voila!

For example, 2^{3} + 3^{3} = 35, so 70^{3} + 105^{3} = 35^{4}.