  ``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.''
  This paper gives an exhaustive summary of Euler's work on the pentagonal
number theorem. I have gone through all of Euler's published correspondence
(except with du Maupertuis and Frederic II) and his papers to find each time he
discusses the pentagonal number theorem or applications of it. I have
translated from the Latin many sections of his correspondence and papers that
are not available in the English, and also sections in the French and German
with Dr. Paul Mezo and Christian Leger.
