Expressing a number as the sum of three perfect cubes is a surprisingly interesting problem. It’s easy to show that most numbers can’t be written as one cube or the sum of two cubes, but it’s ...

After years of work, there was only one number left below 100 that hadn't been proven to be the sum of three cubes. A million+ hours of worldwide supercomputer time later, even mighty 42 has fallen.

If you notice that the first term is a perfect square, and the second term is a perfect square, and you have a negative here, we can say that it is "the difference of two squares." What we want to do ...

Abstract Let R (n) denote the number of representations of a large positive integer n as the sum of two squares, two cubes and two sixth powers. In this paper, it is proved that the anticipated ...