Question

Express the greatest common divisor of the following pair of integers as a linear combination of the integers.
17, 213

Answer 1

It's clear that the \(\gcd\) is \(1\).

Answer 2

Hmm, let's see if I am able to find a linear combination.

Answer 3

yeah that is what I got too but can not figure out the linear combination

Answer 4

Hmm, so I figured it by guess work: \( 1 = -25\times17 + 2\times213\)

Answer 5

thank you