Question

Find the remainder of 3^123 when divided by 7

Answer 1

Answer:

852

Step-by-step explanation:

this is correct answer

Answer 2

Given:

The number 3^123 is divided by 7

Find:

Remainder

Solution:

using modulo for remainder

3 = -4 (mod 7)

3^2 = 2 (mod 7)

3^3 = -1 (mod 7)

we have

$3^{123}=3^{3(41)}$

similarly 3^123=(-1)^41 (mod 7)

3^123=(-1) (mod 7)

In mod7,  -1 will similar as 7-1 = 6

Therefore the remainder will be 6.