JMO --- Divisibility test

When (63⁶³ +63) is divided by 64, the remainder is........................

for JMO STD VII and STD VIII

Answer:

(63⁶³ +63) = (63⁶³ + 1) + 62 = (63⁶³ + 1⁶³) + 62

Now, (xⁿ + aⁿ) is always divisible by (x + a) if "n" is odd.

So, (63⁶³ +1⁶³) is always divisible by 63 + 1 = 64

So, the Remainder is 62.