Euler and number theory (Q5920680)

The paper represents an expanded version of a lecture delivered by the author at the conference dedicated to the 300th birthday of L. Euler at the Steklov Mathematical Institute (2007). It gives an account of important results of L. Euler on number theory, with some emphasize on its analytic aspects, and describes developments which arose from Euler's contributions. Especially, the following topics are discussed: perfect and amicable numbers, Fermat numbers, Euler's totient function, quadratic reciprocity, sums of squares, Pell equation, Diophantine equations related to special number rings, irrational and transcendental numbers, polynomials and primes, zeta series and \(L\)-series, partitions and generating series. The paper contains a wealth of carefully prepared information about many aspects of number theory and its development; it is an important contribution to the history of science.