Python program for Carmicheal Number (#6864)

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Python program to determine whether a number is Carmichael Number or not.

* Rename Carmichael Number.py to carmichael number.py

* Rename carmichael number.py to carmichael_number.py

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* Update carmichael_number.py

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* Update maths/carmichael_number.py

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Christian Clauss <cclauss@me.com>

maths/carmichael_number.py

@@ -0,0 +1,47 @@
+"""
+== 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 isCarmichaelNumber(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 isCarmichaelNumber(number):
+        print(f"{number} is a Carmichael Number.")
+    else:
+        print(f"{number} is not a Carmichael Number.")