Representation of an integer by x2 + Dy2
Keywords:
Quadratic form, prime number, Legendre symbol, quadratic residue
Abstract
In this paper we give the necessary conditions for a old prime number or its opposite number to be of a binary quadratic form x2 + Dy2 with the intergers D where −D is prime number in the interval [5; 23]. Then we give the necessary and sufficient conditions for an integer to be represented by this form.
