[seqfan] Re: (no subject)

[Max Alekseyev]

On Fri, Apr 23, 2010 at 2:02 PM, Emeric Deutsch <deutsch at poly.edu> wrote:

> Given positive integers n, p, q,  p,q <= n, do we have
> a statement about the number of lattice points (t,s)
> satisfying t >= 0, s >= 0, and pt + qs <= n ?

I doubt there is a simple formula. But there is one for pt + qs = n
with coprime p,q:
the number of nonnegative solutions is
floor(n*v/p) + floor(n*u/q)
where u,v are Bezout coefficients: u*p + v*q = 1.

Max