7 Euler's Generalization and ϕ-function
“Mathematicians have tried in vain to this day to discover some order in the sequence of prime numbers, and we have reasons to believe that it is a mystery into which the human mind will never penetrate.”
– Leonhard Euler
7.1 Introduction
Fermat’s work does not contribute much to the mathematics of his own day but creates a lasting impression on later generations of mathematics and Leonhard Euler (1707 – 1783) was the first one to appreciate its significance. Many theorems(without proof) were proclaimed by Fermat, and were later on proved by Euler with the similar arguments formulated by him.
Present chapter deals with Euler’s generalization of Fermat’s Little Theorem, depending on a function which ...
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