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尤拉函數 Euler’s totient function

最大公因數: quicklatex.com-fa826b2ae38f548b52a9703bb8c0590a_l3 尤拉函數 Euler's totient function,可以利用gcd判斷兩個整數是不是互質: quicklatex.com-621912fdd95b3fd8092f7dcc50fa5798_l3 尤拉函數 Euler's totient function,若兩數互質代表兩數的最大公因數就是1。

一個合成數quicklatex.com-8cef6b4f4f69246484c07bb5de49b6a5_l3 尤拉函數 Euler's totient function可以拆成質數分解: quicklatex.com-8fe6774b946463f574a6a5c6118e592f_l3 尤拉函數 Euler's totient function,每個quicklatex.com-1b59fd25aed1ecf6146b4460c9dc464d_l3 尤拉函數 Euler's totient function都只會出現一次。

有了前面幾種工具,就可以建構出尤拉函數:

quicklatex.com-be0181bc295340852afdf0ab76e180ea_l3 尤拉函數 Euler's totient function

尤拉函數能夠幫助我們快速找出在quicklatex.com-8cef6b4f4f69246484c07bb5de49b6a5_l3 尤拉函數 Euler's totient function之下所有與quicklatex.com-8cef6b4f4f69246484c07bb5de49b6a5_l3 尤拉函數 Euler's totient function互質的整數個數。

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I'm Scientia, currently a graduate student. My research interests include Cryptology, Cryptographic Engineering, Security and Privacy, Computational Complexity, Quantum Cryptography, Hardware Security, Cybersecurity and Anomaly Detection.

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