Unpublished paper, 'Certain properties of the arithmetical series, whose 1st, 2nd etc differences are constant; including Fermat's theorem of the polygonal numbers, and some other properties of numbers' by Sir Frederick Pollock

Description

Pollock investigates certain properties of the series of whole numbers whose ultimate differences are constant. His aim is to show that the same (or an analogous) property which Fermat discovered in the polygonal numbers belongs to other series of the same order, also to all series of the first order, and probably to all series of all orders. He also proposes to prove the first case of Fermat’s theorem (that is of the triangular numbers) from the second case of the squares (which had not before been done), and to dispense with the elaborate proof of Legendre (Théorie des Nombres), finally, to prove all the cases by a method different from that either of [Joseph-Louis] Lagrange, [Leonhard] Euler, or [Adrien-Marie] Legendre.

Annotations in ink throughout.

Subject: Mathematics

Received 14 June 1849.

Written by Pollock at Guilford Street [London].

Whilst the Royal Society declined to publish this paper in full, an abstract of the paper was published in volume 5 of Abstracts of the Papers Printed in the Philosophical Transactions of the Royal Society of London [later Proceedings of the Royal Society] as 'On certain properties of the arithmetical series whose ultimate differences are constant'.

Reference number

AP/31/12

Earliest possible date

14 June 1849

Physical description

Ink on paper

Page extent

60 pages

Format

Manuscript