X, x+2 - two consecutive odd or even numbers
Add the reciprocals of these numbers.
Now add the squares of the numerator and denominator, as in the example.
So this number has to be a perfect square.
It is a perfect square, so this method always works.
The numbers
are a Pythagorean triple for any 
.
Add the reciprocals of these numbers.
Now add the squares of the numerator and denominator, as in the example.
So this number has to be a perfect square.
It is a perfect square, so this method always works.
The numbers