first we think of the factors of 21 that are integers. ok, we can have 21 = 1*21 or 21 = 7*3. now, file that away, we'll come back to it.

Now ........the difference of two squares

now we want and to be integer factors of 21.

Let's say they are 7 and 3.

set

and

this is one solution, there are others.

we get a new solution set if a + b = 3 and a - b = 7

and also, if we take the factors to be 1 and 21

we need more conditions if we want a unique solution