#### notes

Consider the following:

`3^2 + 4^2 = 9 + 16 = 25 = 5^2`

The collection of numbers 3, 4 and 5 is known as Pythagorean triplet.

For any natural number m > 1,

we have `(2m)^2 + (m^2 – 1)^2 = (m^2 + 1)^2`.

So, `2m, m^2 – 1` and `m^2 + 1` forms a Pythagorean triplet.