Investigate Fermat's Little Theorem and Euler's Totient Function, including their formulations, applications in cryptography, and relationships to prime numbers and modular arithmetic.
Fermat's Little Theorem: Statement: If ( p ) is a prime number and ( a ) is an integer not divisible by ( p ), then ( a^{p-1} \equiv 1 \pmod{p} ). Key Points: Fermat's Little Theorem is a fundamental result in number theory. It provides a simple way to test if a number is prime. The theorem is particularly useful in cryptography and computer science. Example: Let's consider ( p = 7 ) and (...…
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