The Euler-Fermat Theorem

Click on the image for a detailed proof

a^{\varphi(m)}\equiv 1 \mod m

The Euler-Fermat Theorem is one of the first results published by Euler regarding this function.

It is one of the most valuable results in mathematics, with several real-life applications, serving as an underlying in the RSA cryptosystem.

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Definition of the Euler Totient Function
Definition of the Euler Totient Function
Average order of the Euler Totient Function
Average order of the Euler Totient Function
Infinite zeros on the Critical Line
Infinite zeros on the Critical Line
Ramanujan's Master Theorem
Ramanujan's Master Theorem
Xi Reflection Formula
Xi Reflection Formula
Relation to the Gamma Function 1
Relation to the Gamma Function 1

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