(Solved): 4. Show that 117 is not a prime number by using Fermat's theorem. 4. Show that 117 is not a prime nu ...

Expert Answer

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4. Fermat's Little Theorem states that if p is a prime number and a is any positive integer less than p, then    is congruent to 1 modulo p.

To show that 117 is not a prime number, we can try to find a number a less than 117 that violates Fermat's Little Theorem.
Let's try a = 2. Then, we have:



Using modular exponentiation, we can calculate: