For readers interested in Pythagorean triplets with Consecutive natural numbers, take any odd number -- say 11 -- and square It. 11 squared = 121 = 2(60)+ 1. Add 60 squared to both sides to get 11 squared + 60 squared = 60 squared + 2(60) + 1 = (60 + 1) squared = 61 squared. What do we get? (11, 60, 61). Works every time. Prove it For a general case.