A short proof of Fermat's two-square theorem given by János Bolyai.
A survey of divisibility tests with a historical perspective.
Alan Baker: una obra transcendente.
Alexander Ostrowski, Über sein Leben und Werk
Aviezri Fraenkel's work in number theory.
Charles Hermite’s stroll through the Galois fields
Although everything seems to oppose the two mathematicians, Charles Hermite’s role was crucial in the study and diffusion of Évariste Galois’s results in France during the second half of the nineteenth century. The present article examines that part of Hermite’s work explicitly linked to Galois, the reduction of modular equations in particular. It shows how Hermite’s mathematical convictions—concerning effectiveness or the unity of algebra, analysis and arithmetic—shaped his interpretation of Galois...
Comments on some formulae of Ramanujan
Das Werk Perrons auf dem Gebiete der diophantischen Approximation.
De partitione numerorum.
Derrick Henry Lehmer
Descente infinie et analyse diophantienne : programmes de travail et mises en œuvre chez Fermat, Levi, Mordell et Weil
Desde los números de Fermat hasta la geometría.
Diophantische Analysis und Modulfunktionen.
Distribution des nombres premiers et fonction
El teorema de Fermat y sus historia.
Évariste Galois and the social time of mathematics
The thrust of this article is to offer a new approach to the study of Galois’s Mémoire sur les conditions de résolubilité des équations par radicaux. Drawing on methodology developed by social and cultural historians, it contextualizes Galois’s work by situating it in the parisian mathematical milieu of the 1820s and 1830s. By reconstructing the social process whereby a young man became an established mathematician at the time, this article shows that Galois’s trajectory was far from unusual, and...
Factor tables 1657–1817, with notes on the birth of number theory
The history of the construction, organisation and publication of factor tables from 1657 to 1817, in itself a fascinating story, also touches upon many topics of general interest for the history of mathematics. The considerable labour involved in constructing and correcting these tables has pushed mathematicians and calculators to organise themselves in networks. Around 1660 J. Pell was the first to motivate others to calculate a large factor table, for which he saw many applications, from Diophantine...
Fermat's theorem in János Bolyai's manuscripts.
FFF. Fibonacci: di Fiore in Fiore
In occasione della commemorazione dell’800-esimo anniversario della pubblicazione del Liber Abaci, desidero richiamare l’attenzione del lettore su alcuni dei fatti che preferisco riguardanti numeri di Fibonacci. Tali fatti includono la presenza di quadrati, di multipli di quadrati e di numeri potenti tra i numeri di Fibonacci, la rappresentazione di numeri reali e la costruzione di numeri trascendenti mediante numeri di Fibonacci, la possibilità di costruire una serie zeta ed un dominio a fattorizzazione...
Franciscus Vieta und die Eulersche Identität (Quaternionen).