New demonstrations about the divisors of numbers of the form xx + nyy
First, Euler presents some familiar theorems about quadratic residues. Then he presents two main theorems: If n is of the form 4k+1 or 4k+2, then the only prime divisors of xx+nyy are of the form 4ni+2n−1; and If n is of the form 4k or 4k−1, then the only prime divisors of xx+nyy are of the form 4ni−2n+1.
Original Source Citation
Nova Acta Academiae Scientiarum Imperialis Petropolitanae, Volume 1, pp. 47-74.
Opera Omnia Citation
Series 1, Volume 4, pp.197-220.