Question

The remainder when 4^101 is divided by 101 is

Answer 1

Step-by-step explanation:

Given The remainder when 4^101 is divided by 101 is

• We have Fermat’s little theorem states that for any prime n and any integer a such that  n^a – n is an integer multiple of a
• So n is a prime number.
• So n^(a – 1) = 1 (mod a)
• Let n = 4 and a = 101 we get
• So 4^(101 – 1) = 1 (mod 101)
• So 4^100 = 1 (mod 101)
• Multiply both sides by 4 we get
• So 4 x 4^100 = 4 (mod 101)
• So a^m x a^n = a^m + n using this we get
•     4^101 = 4 (mod 101)
• Therefore 4^101 will have a remainder 4 when divided by 101.

Reference link will be

https://brainly.in/question/5477715

https://brainly.in/question/16107102