Consider the following problem: The difference of the squares of two numbers is the same as their sum. What numbers satisfy this condition?


We might begin by expressing the problem as an equation: Then we can look for possible solutions. Let's try to simplify the expression:

Solving for a:

So, any adjacent natural numbers, n and n+1, will satisfy the conditions of the problem. Thus,

For example,

or

If we pick odd squares, then we can generate an infinite number of Pythagorean triples, for example:

or