From: Robin Chapman Newsgroups: sci.math Subject: Re: question: representation of pos. int.'s as sums of squares Date: Tue, 08 Dec 1998 10:25:36 GMT In article <19981207234801.21438.00003744@ng43.aol.com>, qbob@aol.com (QBOB) wrote: > I know the conditions for a given non-negative integer being the sum of 2 or > less squares and 3 or less squares (and of course all are the sum of 4 or less > squares), and I know the formulas for the number of representations as a sum of > 2,4,6, or 8 squares (counting permutations and sign changes as different), and > I also know that there exist formulas for the number of sums of an odd number > of squares, but I don't know what they are. Please either send me the formulas > for 3,5, and 7 squares, or send me an internet site with good information of > this topic. Please do not send references to books or other printed materials > as I do not have access to such references (being in high school and all). > I'm sorry but the best reference I know is a book: Emil Grosswald's Representations of Integers as Sums of Squares (Springer 1985). The formula for 3 squares involves class numbers and is due to Gauss. He proved that for n > 3 the number R_3(n) of *primitive* representations as a sum of three squares is 12 h(-4n) for n = 1 or 2 (mod 4) and 24 h(-n) if n = 3 (mod 4) where h(-k) is the number of reduced positive definite binary quadratic forms of discriminant -k. Robin Chapman + "They did not have proper SCHOOL OF MATHEMATICal Sciences - palms at home in Exeter." University of Exeter, EX4 4QE, UK + rjc@maths.exeter.ac.uk - Peter Carey, http://www.maths.ex.ac.uk/~rjc/rjc.html + Oscar and Lucinda, chapter 20 -----------== Posted via Deja News, The Discussion Network ==---------- http://www.dejanews.com/ Search, Read, Discuss, or Start Your Own