Another Exponent / Remainder Question

[mlaboda]

If X is a positive integer, what is the remainder when (2^8x+2)+6 is divided by 5?

[chetanojha]

Check below.

[bharathh]

Remainder is always 4

Just consider the units digit for this question. Rest is not required.

2^8 = 256
256^x will always have units digit 6... 6 + 2 will make the units digit 8

Add 6 to that... and units digit will be 4

When a number having a units digit of 4 is divided by 5 remainder will always be 4

[vittalgmat]

This is a relatively old problem that I came across.

I always get the remainder as 0.
Pls let me know if I am missing something.

eg. if x = 1
then the expr becomes 2^10 ==> 1024 ==> units digit is 4
Add 6 to this. The unit digit becomes 0 which is always divisible by 5.