Codes Hunger

Curzon Numbers

In this challenge, establish if a given integer num is a Curzon number. If 1 plus 2 elevated to num is exactly divisible by 1 plus 2 multiplied by num, then num is a Curzon number.

Given a non-negative integer num, implement a function that returns True if num is a Curzon number, or False otherwise.

Examples

is_curzon(5) ➞ True

# 2 ** 5 + 1 = 33

# 2 * 5 + 1 = 11

# 33 is a multiple of 11

is_curzon(10) ➞ False

# 2 ** 10 + 1 = 1025

# 2 * 10 + 1 = 21

# 1025 is not a multiple of 21

is_curzon(14) ➞ True

# 2 ** 14 + 1 = 16385

# 2 * 14 + 1 = 29

# 16385 is a multiple of 29