When ( 67^67 + 67 ) is divided by 68 , the remainder will be :

a 1

b 63

c 66

d 67

[SSC EXAM 2011]

We have to find the remainder when (67⁶⁷ + 67) is divided by 68.

Let us try it with the simple numbers in the beginning.

Find the remainder when (2² + 2) is divided by 3.

We have, 2² + 2 = 6 which leaves remainder 0 when divided by 3.

Again take (3³ + 3) divide by 4.

We have, 30 divided by 4.

The remainder will be 2 (which is 3 – 1).

If we take , the remainder will be 0.

If we take , the remainder will be 5 – 1 = 4.

In this way, if we take the odd number and divide it by even, the remainder is 1 less than the odd number.

So, the remainder when 67⁶⁷ + 67 is divided by 68 will be 67 – 1 = 66.