Find a Pythagorean triplet whose one member is 6.

We know that the Pythagorean triplets can be found by using the general form 2m, m² − 1, m² + 1, where m is a natural number greater than 1.

If m² − 1 = 6

⇒ m² = 6 + 1 = 7

Then, the value of m will not be an integer.

If m² + 1 = 6

⇒ m² = 6 − 1 = 5

Then, the value of m will not be an integer.

Therefore, let 2m = 6

⇒ m = 3, which is a natural number greater than 1

∴ m² − 1 = 3² − 1 = 9 − 1 = 8,

m² + 1 = 3² + 1 = 9 + 1 = 10,

Therefore, the required Pythagorean triplet is 6, 8 and 10.