Which of the following is a Pythagorean triplet whose smallest number is 8?

Concept

A Pythagorean triplet consists of three positive integers a, b, and c that satisfy a2 + b2 = c2, where c is the largest number.

A candidate set is valid only when the squares of its two smaller numbers add exactly to the square of its largest number.

Application

1. Take a = 8, b = 15, and c = 17 for the candidate set 8, 15, 17.

2. Compute the left side: 82 + 152 = 64 + 225 = 289.

3. Compute the right side: 172 = 289. Both sides are equal, and 8 is the smallest member.

Cross-check

Euclid's formula (m2 − n2, 2mn, m2 + n2) with m = 4 and n = 1 gives (15, 8, 17), independently producing the same three numbers.

Result

Therefore, the required Pythagorean triplet is 8, 15, 17.