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4. Show that 117 is not a prime number by using Fermat's theorem.

4. Show that 117 is not a prime number by using Fermat's theorem. 5. Calculate $τ(100)$ using the formula given in the textbook.

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:

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