Isn’t it just 1/gcd({N_r})? By analogy with the case r=2, where any large enough multiple of the gcd is expressible with non-negative coefficients (at least that is the way I remember it), which means that the density is 1/gcd (since all linear combinations are multiples of the gcd) Sent from my iPhone
On Dec 18, 2020, at 23:25, Dan Asimov <asimov@msri.org> wrote:
Let N_1, ..., N_r be a set of positive integers ≥ 2 whose prime factorizations are known.
Let X = {∑ c_j N_j} be the set of all linear combinations of the N_j with nonnegative integer coefficients c_j.
Is it easy to determine what the (asymptotic) density of X is in Z+ ???
(An N_j may have repeated prime factors, and several N_j's may have common factors.)
—Dan _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun