1. Consider the group Zp for a prime p with multiplication multiplication mod p). Show that...

1. Consider the group Zp for a prime p with multiplication multiplication mod p). Show that (p − 1)2 = 1 (mod p)

2. Is the above true for any number (not necessarily prime)?

3. Show that the equation a 2 − 1 = 0, has only two solutions mod p.

4. Consider (p − 1)!. Show that (p − 1)! = −1 (mod p) Remark: Think about what are the values of inverses of 1, 2, . . . , p − 2.

Expert Solution

Colby Messinger answered 2 years ago

If p is prime, then Z*p is a group under multiplication.

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