Question

Let N = 640640640643, without actual computing N 2 , prove that N 2 leaves 1 as remainder when divided by 8. ANSWER A.S.A.P

Answer 1

first of all we know that ant number will be divisible by 2 when ones of that number be 0,2,4,6,8
so we divide 3 by 2 we get 1 remainder

Answer 2

Given

N = 64064060643,

As we know that to check the dividibility of number 8 we need only last 3 digits . So, here given last 3 digits are

643.

When 643 is divisible 8 we get reminder as 3.

So now N = 3 ( N/8 gave the reminder 3 therefore N = 3)

Next it is asked that to prove the square of N when divided by 8 leaves reminder as 1, therefore let's square 'N'.

N = 3

N² = 3²

N²/8 = 3²/8

N²/8 = 9/8

9/8 gives the reminder 1.

So N² gave the reminder 1.

Hence Proved.

Hope it helps!!!!