1. Consider the group Zp for a prime p with multiplicationmultiplication 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 solutionsmod 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.
