We know that, Fermat Showed a prime can be expressed as a sum of two squares if and only if it is a multiple of four plus one and its decomposition is unique. This paper will discuss the similar writings of primes as a sum of squares and multiple of another square.

Periodical:

The Bulletin of Society for Mathematical Services and Standards (Volume 3)

Pages:

67-72

DOI:

10.18052/www.scipress.com/BSMaSS.3.67

Citation:

K. R. R. Gandhi "Primes of the form x^{2 }+ ny^{2}", The Bulletin of Society for Mathematical Services and Standards, Vol. 3, pp. 67-72, 2012

Online since:

Sep 2012

Authors:

Keywords:

Distribution:

Open Access

This work is licensed under a

Creative Commons Attribution 4.0 International License

References:

http: /arxiv. org/pdf/1207. 0172v1. pdf.

http: /en. wikipedia. org/wiki/Fermat%27s_theorem_on_sums_of_two_squares.

C. Edward Sandifer, How Euler did it, The Mathematical Association of America, (2007).

Hans Riesel, Prime Numbers and Computer Methods for Factorization, Birkhauser, second edition, Springer Sciences + Business media. Sweden.

Franz Lemmermeyer, Reciprocity Laws: From Euler to Eisenstein, Springer Verlag.

Richard Dedekind, Theory of Algebraic Integers, Cambridge Mathematical Library, (1996).

Sergiu Rudeanu, Lattice Functions and Equations, Springer Verlag, (2001).

Martin Aigner, Günter M. Ziegler, Proofs from The Book, Springer Verlag.

Bhubaneswar Mishra, Algorithmic Algebra, Springer Verlag, New York, (1993).

James J. Tattersall, Elementary Number Theory in Nine Chapters, Second edition, CUP.

M.R. Adhikari, A. Adhikari, Groups, Rings And Modules With Applications, University Press (India) Limited, (2003).