1. Using the Extended Euclidean algorithm, compute (by hand) gcd(n, m) and integers x, y such that xn + ym = gcd(n, m) for the following pairs of numbers: 2. Prove the following extensions to Lemma...

1. Using the Extended Euclidean algorithm, compute (by hand) gcd(n, m) and integers x, y such that xn + ym = gcd(n, m) for the following pairs of numbers:

2. Prove the following extensions to Lemma 7.10

There are infinitely many pairs of integers x, y such that xn + ym = gcd(n, m), for any nonnegative integers n and m.