Find the value of 7^2019 MOD 13 using Fermat’s Little theorem. Define Euler totient function with
an example.

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Find the value of 7^2019 MOD 13 using Fermat&#8217;s Little theorem. Define Euler totient function with an example.

Suresh Chand · Accepted Answer

Solution: Now, 72019 mod 13 From Femat's Little theorem, 713 - 1 = 1 (mod 13) or, 712 = 1 (mod 13) and, 713 = 7 (mod 13) Also, = 72019 (mod 13) = (712)168 (mod 13) = (1)168 x 73 (mod 13) = 73 (mod 13) = 343 (mod 13) = 5 (mod 13) Euler's Totient Function: Euler's Totient function Φ(n) for an input n is count of positive intergers in {1, 2, 3, . . . . , n-1} that are relatively prime to n, i.e. the positive integers whose GCD with n is 1. Examples: Φ(1) = 1; gcd (1, 1) is 1 Φ(2) = 1; gcd(1, 2) is 1, but gcd(2, 2) is 2. Φ(3) = 2; gcd(1, 3) is 1, and gcd(2, 3) is 1. Φ(4) = 2; gcd(1, 4) is 1 and gcd(3, 4) is 1 Φ(5) = 4; gcd(1, 5) is 1, gcd(2, 5) is 1, gcd(3, 5) is 1 and gcd(4, 5) is 1

Find the value of 7^2019 MOD 13 using Fermat’s Little theorem. Define Euler totient function with
an example.

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Find the value of 7^2019 MOD 13 using Fermat’s Little theorem. Define Euler totient function with an example.

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Find the value of 7^2019 MOD 13 using Fermat’s Little theorem. Define Euler totient function with
an example.