# Today I Learned

Some of the things I've learned every day since Oct 10, 2016

## Category Archives: number theory

## 96: Euler’s Theorem (Number Theory)

January 20, 2017

Posted by on **Euler’s Theorem** is a sort of extension of Fermat’s Little Theorem. One way of stating Fermat’s is that where is prime and is any integer,

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whereas Euler’s Theorem makes the more general statement that if are simply two *coprime* integers and is Euler’s totient function,

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The reason Fermat’s is a valid special case of Euler’s is because when is prime, .

[The congruence in the statement of Euler’s theorem is actually equivalent (‘if and only if’) to being coprime.]

## 65: Completely Multiplicative Functions

December 16, 2016

Posted by on In number theory, a **completely multiplicative **function is a multiplicative function satisfying the stronger condition that for *any* two .

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