User stemkoski - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-25T21:14:40Z http://mathoverflow.net/feeds/user/27497 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/111489/the-quadratic-form-x2ny2-via-prime-factors The quadratic form $x^2+ny^2$ via prime factors Stemkoski 2012-11-04T22:00:15Z 2012-11-05T03:53:41Z <p>Elementary algebra shows that the product of two numbers in the form $x^2 + ny^2$ again has the same form, since if $p = (a^2 + nb^2)$ and $q = (c^2 + nd^2)$, $$pq = (a^2 + nb^2)(c^2 + nd^2) = (ac \pm nbd)^2 + n(ad \mp bc)^2$$ My question is: Assuming that a number $z$ can be factored into primes of the form $x^2 + ny^2$, does <em>every</em> representation of $z$ in this form arise from repeated applications of this formula to the prime factors? </p> http://mathoverflow.net/questions/88102/where-is-the-euler-goldbach-correspondence/110470#110470 Answer by Stemkoski for Where is the Euler/Goldbach correspondence? Stemkoski 2012-10-23T20:36:49Z 2012-10-23T20:36:49Z <p>The Euler-Goldbach correspondence has been included in the Euler Archive, part of the MAA digital library, at:</p> <p><a href="http://eulerarchive.maa.org/correspondence/correspondents/Goldbach.html" rel="nofollow">http://eulerarchive.maa.org/correspondence/correspondents/Goldbach.html</a></p>