Purists may protest that Fermat’s Last Theorem isn't strictly

Software 241 Purists may protest that Fermat’s Last Theorem isn't strictly Diophantine because it refers to a variable exponent — the x to the n part. This is hair splitting. But, of course, the splitting of hairs is bread and butter to a mathematician. We will see later that Fermat’s Theorem can be made Diophantine, but we are jumping ahead of ourselves a little. A question that taxed mathematicians for many centuries was whether there are triples for higher powers, such as cubes. In other words, would the cube of the hypotenuse be equal to the sum of the cubes of the other two sides for some set of numbers? After much work, it was proven no triple exists which can solve the cubic equation. But what happens if we substitute higher indices? The next shape to consider is the hypercube — a four-dimensional cube. That may stretch your visual imagination but the equation is simple, 34444454, Again the challenge is to find a whole number solution for: Hypercube HOUSE_OVERSIGHT_015931