We all know of this theorem which was finally proved in the 1960's. It says that we cannot find any real integral solution for n>2 when an integer is expressed to a power of 'n' and is equal to the sum of two numbers which individually are raised to the power 'n'. x^n=a^n+b^n Well for n=2, we are familiar with the pythagorean(3,4,5 etc.) combinations, but there is indeed is no solution when n>2...check it out. I recently ran a program to find this solution, but couldn't find for n=3,4,5... This certainly validates the theorem but how do we prove it mathematically?