Problem 1. a) Determine the number of invertible elements in the monoid $(\mathbb{Z}_{2014}, \cdot)$

b) Prove that the set of all invertible elements in the aforementioned monoid is an abelian group.
Problem 1. a) Determine the number of invertible elements in the monoid ( $Z_{2014}$, )

b) Prove that the set of all invertible elements in the aforementioned monoid is an abelian group.

GRADING: a) An element is invertible if and only if it is coprime with 2014. Therefore, we have 936 invertible elements

b) The product of two invertible elements is invertible, and the inverse of an invertible element is also invertible. Clearly, multiplication is commutative and associative $3 p$