Question

Prove that if p is prime then every element of \( (\mathbb{Z_p}-\{0\}, \cdot ) \) has an inverse

Answer 1

group theory??

Answer 2

yupp

Answer 3

isn't Zp going to be set of prime number??

Answer 4

ohhh i found some hint
Suppose \( x \in \mathbb{Z_p}-\{0\} \). then x and p are relatively prime so there exists intgers r and s such that rx+sp=1