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  3. 1. consider the group zp for a prime p with multip

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

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Advance Math

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.

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