Python/maths/carmichael_number.py

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"""
== Carmichael Numbers ==
A number n is said to be a Carmichael number if it
satisfies the following modular arithmetic condition:
power(b, n-1) MOD n = 1,
for all b ranging from 1 to n such that b and
n are relatively prime, i.e, gcd(b, n) = 1
Examples of Carmichael Numbers: 561, 1105, ...
https://en.wikipedia.org/wiki/Carmichael_number
"""
def gcd(a: int, b: int) -> int:
if a < b:
return gcd(b, a)
if a % b == 0:
return b
return gcd(b, a % b)
def power(x: int, y: int, mod: int) -> int:
if y == 0:
return 1
temp = power(x, y // 2, mod) % mod
temp = (temp * temp) % mod
if y % 2 == 1:
temp = (temp * x) % mod
return temp
def is_carmichael_number(n: int) -> bool:
b = 2
while b < n:
if gcd(b, n) == 1 and power(b, n - 1, n) != 1:
return False
b += 1
return True
if __name__ == "__main__":
number = int(input("Enter number: ").strip())
if is_carmichael_number(number):
print(f"{number} is a Carmichael Number.")
else:
print(f"{number} is not a Carmichael Number.")