Interview Question: 2^n - 1 divide by 7 | Algorithms, Blockchain and Cloud

Q: n is a none-negative numbers, in order to let $tex_a9973c04ccf3c7ed4be19df22022e2cc Interview Question: 2^n - 1 divide by 7$ divides perfectly 7, characterise n.

A: $tex_a9973c04ccf3c7ed4be19df22022e2cc Interview Question: 2^n - 1 divide by 7$ in binary representation is n ones. And 7 in binary is 111. The n has to be multiples of 3 in order for $tex_af6556883f4df6cc17ebd9d1c6279c4b Interview Question: 2^n - 1 divide by 7$ to be zero.

The following python script proves this by output the first then n (excluding zero because it is so obvious)

#!/usr/bin/python

cnt = 0
n = 1

while 1:
	if (2**n - 1) % 7 == 0:
		cnt += 1
		print n
		if cnt > 10: break
	n += 1

It will output 3, 6, 9, 12 … 33. $tex_dc81441c43f1d8405fd57f131dbf55f1 Interview Question: 2^n - 1 divide by 7$ can be replaced by bit logics operation $tex_e946cc9b90780ae5c6641f89065831bd Interview Question: 2^n - 1 divide by 7$ , which is a lot faster.