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* Deleted greatest_common_divisor def from many files and instead imported the method from Maths folder * Deleted greatest_common_divisor def from many files and instead imported the method from Maths folder, also fixed comments * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * Deleted greatest_common_divisor def from many files and instead imported the method from Maths folder, also fixed comments * Imports organized * recursive gcd function implementation rolledback * more gcd duplicates removed * more gcd duplicates removed * Update maths/carmichael_number.py * updated files * moved a file to another location --------- Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com> Co-authored-by: Tianyi Zheng <tianyizheng02@gmail.com>
41 lines
1.1 KiB
Python
41 lines
1.1 KiB
Python
"""
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== Carmichael Numbers ==
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A number n is said to be a Carmichael number if it
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satisfies the following modular arithmetic condition:
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power(b, n-1) MOD n = 1,
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for all b ranging from 1 to n such that b and
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n are relatively prime, i.e, gcd(b, n) = 1
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Examples of Carmichael Numbers: 561, 1105, ...
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https://en.wikipedia.org/wiki/Carmichael_number
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"""
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from maths.greatest_common_divisor import greatest_common_divisor
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def power(x: int, y: int, mod: int) -> int:
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if y == 0:
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return 1
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temp = power(x, y // 2, mod) % mod
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temp = (temp * temp) % mod
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if y % 2 == 1:
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temp = (temp * x) % mod
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return temp
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def is_carmichael_number(n: int) -> bool:
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b = 2
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while b < n:
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if greatest_common_divisor(b, n) == 1 and power(b, n - 1, n) != 1:
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return False
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b += 1
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return True
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if __name__ == "__main__":
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number = int(input("Enter number: ").strip())
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if is_carmichael_number(number):
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print(f"{number} is a Carmichael Number.")
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else:
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print(f"{number} is not a Carmichael Number.")
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