Pythagorean Triples and Fermat’s Last Theorem

The Pythagorean theorem says that the sum of the squares of the sides of a right triangle equals the square of the hypotenuse. In symbols, a2 + b2 = c2. Since we are interested in Number Theory, that is, the theory of whole numbers, we ask if there are any Pythagorean triangles whose sides are whole numbers. There are many such triangles, the most famous being 3, 4, and 5, and the next being 6, 8, and 10, the ones carpenters use to “square-a-house”, since they know that the converse of the Pythagorean theorem is true. Here are a few more examples