Find different negative integers $a$ and $b$ which satisfy the following:
(a) $\gcd (a, b) = 5$
(b) $\gcd (a, b) = 100$
(c) $\gcd (a, b) = 169$
We can do this exercise by using the negation of the gcd as one of the negative integers, and then for the second we can multiply that negative integer by a prime number such that is not a factor of it.
(a) $\gcd (-5, -10) = 5$
(b) $\gcd (-100, -200) = 100$
(c) $\gcd (-169, -338) = 169$