Question

determine the remainder when 48^37 is divided by 7.​

Answer 1

Answer:

We know that

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.

HOPE IT HELPS..!!

Answer 2

Answer:

remainder is 6

Step-by-step explanation:

48^37

here 8 cyclicity is 2

So, divide 37 by 2 gives remainder 1

Now, 48^1 =48

Hence, 48/7 = 6 as remainder

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