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
