what is the remainder in 2^256/17 ?

Question

What is the easy way of solving such problem ? Please explain the theory if possible. Thank you

Answer 1

This is a brainteaser and I won't let it tease my brain :))

It is really simple in fact. 256 / 17 = 15.058823529411764705882352941176.

Round it down and you will get 15.

Now calculate this to get the remainder:

256 - (17*15) = 256 - 255 = 1

The remainder of 2^256/17 is 1.

Good luck.

Answer 2

theory see : fermat's little theorem.

2^1 / 17 => remainder2
2^2 / 17 => 4
2^3/17 => 8
2^4/17 => 16 ( which is also -1 )
2^5 = 2^4 * 2 = -1 * 2 = -2 ( which is also 15 )
2^6 = 2*-2 = -4
2^7=2*-4 = -8
2^8 = 2*-8 = -16 = 1

so after 8 times you have remainder =1
reduce 256 : 256/8 remainder = 0 thus 2^256/17has remainder 1

Answer 3

= 6.8113 x10^75
answer would be 6 w/ remainder 8.113x10^74...I guess