Bàyer, Pilar Some observations on infinite series. (Catalan) Zbl 0598.10002 Butll. Soc. Catalana Ciènc. Fís. Quím. Mat. 2, 429-481 (1984). This article belongs to a collection of papers dedicated to L. Euler’s bícentennial (1707–1783) and surveys Euler’s contributions to elementary and analytic number theory. Chapter headings are roughly: (1) Introduction; (2.1)-(2.5) Perfect numbers, Fermat numbers, continued fractions; Fermat’s equation and other Diophantine equations, Euler and Bachet; (3.1)-(3.6) Riemann’s zeta-function; functional equation; gamma function; further development of Euler’s ideas: B. Riemann; the zeta- function and the prime number theorem; (4) Origins of the theory of partitions. MSC: 11-03 History of number theory 01A50 History of mathematics in the 18th century Biographic References: Euler, L.; Riemann, B. PDFBibTeX XMLCite \textit{P. Bàyer}, Butll. Soc. Catalana Ciènc. Fís. Quím. Mat. 2, 429--481 (1984; Zbl 0598.10002)