Take two integers that differ by two, e.g. as 3 and 5.
Create their reciprocals and add them: 1/3 + 1/5 = 8/15.
The numerator and the denominator in the resulting sum are always two numbers of a Pythagorean triplet!
In our case the Pythagorean triplet is 8, 15, 17.

Explain why it always works.