Question

When 4^128 divided by 17, the remainder would be​

Answer 1

Answer:

1

Step-by-step explanation:

4²=-1(mod 17)

(4²)^64=(-1)^64(mod 17)

therefore 4^128=1(mod 17)

thus reminder is 1..

easily done!!

Answer 2

Concept:

Two integers a and b are said to be congruent modulo an integer n, referred to as a modulus, if n is a divisor of their difference (i.e., if there is an integer k such that a b = kn).

A congruence relation is an equivalence relation that is compatible with addition, subtraction, and multiplication. Congruence modulo n is one such relation. The symbol for congruence modulo n is:

a≡k (mod b)

Given:

When 4^128 divided by 17,

Find:

the remainder would be​

Solution:

Using congruence modulo theroem,

4²≡-1(mod 17)

(4²)⁶⁴≡(-1)⁶⁴(mod 17)

4¹²⁸≡1(mod 17)

Therefore, remainder is 1

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