Answer :
The computation of 3^141 (mod 31) using fast exponentiation requires certain values. The second part of the answer will provide an explanation of the values needed and the computation process.
To compute 3^141 (mod 31) using fast exponentiation, we need the following values:
1. The base, which is 3 in this case.
2. The exponent, which is 141.
3. The modulus, which is 31.
Fast exponentiation is an efficient algorithm that reduces the number of multiplications required to compute a large exponentiation by using the property of modular arithmetic. The algorithm works by repeatedly squaring the base and taking the remainder with the modulus.To compute 3^141 (mod 31) using fast exponentiation, we follow these steps:
1. Initialize a variable, let's call it result, to 1.
2. Convert the exponent (141) to binary form, which is 10001101.
3. Iterate through the binary digits from left to right. For each digit:
a. Square the result and take the remainder with the modulus (31).
b. If the current binary digit is 1, multiply the result by the base (3) and take the remainder with the modulus (31).
4. After iterating through all the binary digits, the final value of the result will be the desired result of 3^141 (mod 31).By applying the fast exponentiation algorithm with the given values, we can compute 3^141 (mod 31) as the final result.
Learn more about algorithm here:- brainly.com/question/33268466
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