Question

Determine the remainder when 48 raised to the power 37 is divided by 7.
Pls explain in detail.

Answer 1

Answer:

6

Step-by-step explanation:

48 = (-1) (mod7)

=) 48^567 = (-1)^567 (mod7)

=) 48^567 = (-1) (mod7) = 6 (mod7)

So the required remainder is 6.

Method 2

Here gcd(48, 7) =1 and 7 is prime

So by Fermat's Little Theorem

48^6= 1 (mod 7)

=) (48^6)^94 = 1^94 (mod7)

=) 48^564 = 1 (mod7)

=) 48^564 . 48^3 = 48^3 (mod7)

=) 48^567= (-1)^3 (mod7)=) 48^567 = (-1) (mod7) = 6 (mod7)

So the required remainder is 6.