Question

Describe the process of using Fermat’s Little Theorem to calculate remainders using a calculator.

Answer 1

Fermat's Little Theorem is a theorem in number theory that allows us to calculate remainders. It states that if p is a prime number and a is any integer not divisible by p, then a raised to the power of p-1 is congruent to 1 modulus p. To calculate remainders using Fermat's Little Theorem with a calculator, enter the base number and prime number, calculate the exponentiation, and divide by the prime number to get the remainder of 1.

Step-by-step explanation:

Fermat's Little Theorem is a theorem in number theory that allows us to calculate remainders. The theorem states that if p is a prime number and a is any integer not divisible by p, then a raised to the power of p-1 is congruent to 1 modulo p. This means that when dividing a^p-1 by p, the remainder will always be 1.

To calculate remainders using Fermat's Little Theorem with a calculator, follow these steps:

1. Enter the base number (a) and the prime number (p) into a calculator.
2. Calculate a raised to the power of (p-1) using the exponentiation function on the calculator.
3. Divide the result by p.
4. The remainder will be 1.