Question

A Pythagorean triple is said to be "primitive" if the greatest common divisor of a, b, and c is 1. Use trial and error to find a primitive Pythagorean triple other than (3, 4, 5).

Answer 1

Disclaimer: I'm not super familiar with this method, I'll link to the original source where I got it from

you pick two positive integers m and n, where m > n (so m could be 2 and n could be 1, for example) and calculate your a, b, and c values with the formulas:

a = m^2 − n^2
b = 2mn
c = m^2 + n^2

to get a pythagorean triple of a,b, and c.

in your case, you'd have to keep trying with integer combinations of m and n until you got a pythagorean triple with no common factors

reference: https://www.mathsisfun.com/numbers/pythagorean-triples.html

Answer 2

oh, right, I forgot to add this before but prime numbers are a good place to start with m and n