Let A ={x ∈Z: 7x ≡13 (mod 17)}. a) Find a number β ∈Zsuch that (7β) mod 17 =1. b) Prove that there exists a number z ∈{0,1,...,16}such that A ={x ∈Z: x mod 17 =z}. c) Find z. (Hint: Use modular arithmetic.)