Thanks,. I figured it was a bit too easy ;) On 4 Jun 2014, at 12:40, Fred Lunnon wrote:
Neil omitted to specify that he is looking for _integer_ solutions. WFL
On 6/4/14, David Makin <makinmagic@tiscali.co.uk> wrote:
Apologies if I've done something stupid here, it's around 30 years since I last did a "proof":
We want to prove real solution/s for:
a*x^2 + b*x*y + c*y^2 = n
If solvable then for some real constant y we have:
a*x^2 + b*x*y + c*y^2 - n = 0
So there are solutions if:
b^2*y^2 - 4*a*(c*y^2 - n) > 0
(b^2 - 4*a*c)*y^2 - 4*a* n > 0
(b^2 - 4*a*c)*y^2 > 4*a*n
Because we know (b^2-4*a*c)>0 and y is real then there is a value of y that will satisfy this therefore there is also a value for x to go with this as a solution to:
a*x^2 + b*x*y + c*y^2 = n
i.e. there is always a solution.
On 4 Jun 2014, at 05:41, Neil Sloane wrote:
Does anyone have a program for doing the following:
Given an indefinite binary quadratic form ax^2+bxy+cy^2 (with discriminant b^2-4ac>0 and not a square) and a positive or negative number n, decide if ax^2+bxy+cy^2 = n has a solution.
(If n = p is a prime, one can use the PARI command qfbsolve(Qfb(a,b,c),p) )
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The meaning and purpose of life is to give life purpose and meaning. The instigation of violence indicates a lack of spirituality. The meaning and purpose of life is to give life purpose and meaning. The instigation of violence indicates a lack of spirituality.