For the following parts, a correct numerical answer will only earn credit if accompanied by
it's derivation. Show your work.
(a) [4 pts] Use the Pulverizer to ?nd integers s and t such that 135s + 59t = gcd(135, 59).
(b) [4 pts] Use the previous part to ?nd the inverse of 59 modulo 135 in the range {1,..., 134}.
(c) [4 pts] Use Euler's theorem to ?nd the inverse of 17 modulo 31 in the range {1,..., 30}.
(d) [4 pts] Find the remainder of 3482248 divided by 83. (Hint: Euler's theorem.)