Which Pythagorean triplet has 16 as its smallest number?

It is known that the numbers that are of the form 2m, m² − 1 and m² + 1, where m is a natural number greater than 1 form a Pythagorean triplet.

Now, we can not take m² + 1 = 16, as then m² + 1 will not be the smallest member of Pythagorean triplet.

If m² − 1 = 16, then m² will be 17

However, m will not be a natural number.

Therefore, let 2m = 16

$m=\frac{16}{2}=8$

∴ m² − 1 = 8² − 1 = 64 − 1 = 63

m² + 1 = 8² + 1 = 64 + 1 = 65

Therefore, the required triplet is (16, 63, 65).