# Tag Archives: Euler

## 고등학생을 위한 오일러 등식의 유도

Euler_Identity.pdf ABSTRACT. In 1990, D. Wells polled readers of The Mathematical Intelligencer, one of the well-known journals on mathematics, to see what they thought was the greatest theorem of all time. The top vote getter was Euler's equation. Since then Euler's equation has been known as the greatest mathematical equation ever and begun to attract not only mathematicians… Read More »

## Euler Phi-Function is a Multiplicative Function

Let $$n$$ be a positive integer. Recall that the Euler phi-function $$\phi(n)$$ is defined as the number of positive integers less than or equal to $$n$$ and relatively prime to $$n.$$ Note that $$\phi(1)=1.$$ We have seen that Euler used this function to generalize the Fermat's Little Theorem. It is sometimes needed to calculate the value $$\phi(n)$$ of… Read More »

## Euler’s Generalization of Fermat’s Little Theorem

Fermat's Little Theorem says: Theorem 1. (Fermat) If $$p$$ is a prime number and $$(a,~p)=1,$$ that is, if $$a$$ and $$p$$ are relatively primes, then $$a^{p-1}\equiv 1$$ $$({\rm mod}~ p).$$ Euler gave a generalization of Fermat's theorem. His generalization will follow at once from next theorem, which is proceed by counting, using essentially the same argument as in… Read More »