CAN YOU SOLVE THIS ???-2

Number Theory Level 1

n=560560560560563.Saket divided n^2 by 8.He will get a remainder _

The answer is 1.

1 solution

Sujoy Roy
Dec 6, 2014

As $560$ is divisible by $8$ , $560560560560$ is also divisible by $8$ .

So, $n^2 \mod 8 = (n \mod 8)^2 \mod 8 = 3^2 \mod 8 = \boxed{1}$