Pierre Fermat and the modern origins of Diophantine analysis (Q2713747)

This article is about Fermat's work performed during the period 1636-40. Its author, a scholar of the subject, presents details of specific topics studied by Fermat, mainly based on the correspondence with Mersenne. He shows that the famous mathematician was relying on two traditions: Euclidean and neo-Pythagorean arithmetics on one hand, Diophantine analysis on the other. The first is concerned with criteria on integer numbers. The second endeavours to introduce demonstrations for algorithms.NEWLINENEWLINENEWLINEThe author wonders whether Fermat might have been directly or indirectly aware of quite earlier pioneering achievements on Diophantine analysis by al-Kwārizmī, the `founder' of Algebra. The `new' Diophantine analysis admits as its domain numerical rectangles; in 1640 Fermat then began studying quadratic forms.