ar X iv : m at h / 05 10 05 4 v 2 [ m at h . H O ] 1 7 A ug 2 00 6 EULER AND THE PENTAGONAL NUMBER THEOREM

In this paper we give the history of Leonhard Euler's work on the pentagonal number theorem, and his applications of the pentagonal number theorem to the divisor function, partition function and divergent series. We have attempted to give an exhaustive review of all of Euler's correspondence and publications about the pentagonal number theorem and his applications of it. Comprehensus: In hoc dissertatione damus historiam operis Leonhardi Eu-leri super theorma numerorum pentagonalium, et eius usus theoremae nu-merorum pentagonalium ad functioni divisori, functioni partitione et seriebus divergentibus. Conati sumus dedisse recensum plenum omnium commerciorum epistolicarum et editionum Euleri circa theorema numerorum pentagonalium et eius applicationum ipsius.