Theorems about the divisors of numbers contained in the form $paa \pm   qbb$
  Euler states without proof statements about the form of prime divisors of numbers of the form aa+Nbb. See Ed Sandifer's How Euler Did It, ``Factors of Forms'', December 2005 at http://www.maa.org/news/howeulerdidit.html for a summary of the paper. 
Leonhard Euler