Fermat's Little Theorem says that for all natural numbers p and integers x, if p is prime then x = x mod p. (i) Show that the statement is wrong, if we drop the assumption that p is prime. [Remember: All you need to do is to give a counterexample.] (ii) Show, by giving an example, that if p is not prime, then xP = x mod p can still be true for some integers x with x –1, 0, 1.

Fermat's Little Theorem says that for all natural numbers p and integers x, if p is prime then x = x mod p. (i) Show that the statement is wrong, if we drop the assumption that p is prime. [Remember: All you need to do is to give a counterexample.] (ii) Show, by giving an example, that if p is not prime, then xP = x mod p can still be true for some integers x with x –1, 0, 1.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.2: Mathematical Induction

Problem 46E: Use generalized induction and Exercise 43 to prove that n22n for all integers n5. (In connection...

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