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 5h comment Non-negative decomposition of a non-negative matrix @DenisSerre I think also known as factor rank 14h revised $\mathsf{GCD}$s of random linear form edited title 18h revised $\mathsf{GCD}$s of random linear form edited body 18h asked $\mathsf{GCD}$s of random linear form 19h reviewed Approve Spectral properties of the Laplace operator and topological properties 19h revised Exact statistics in the Frobenius coin problem edited body 20h revised Exact statistics in the Frobenius coin problem added 237 characters in body 20h comment Exact statistics in the Frobenius coin problem No I did not say that is the range I am most interested. I am interested in how the numbers change as we vary $m$. It seems lower the $m$, there are more non-representable numbers and they should be more representable numbers close to $g(a,b)$ to get upto half the numbers to be representable. What exactly is this distribution? 21h revised Probability distribution associated with total divisors of an integer added 54 characters in body 21h revised Exact statistics in the Frobenius coin problem added 223 characters in body 21h comment Exact statistics in the Frobenius coin problem I want to get good approximation to $f_{a,b}(m)$ at every non-negative $mc'ab$ for some $c,c'>0$. Actually I am not sure how to interpret error terms in these kind of calculations. Could you please add a line or two? my first guess is $m>ab$ but since $\min(a,b)<\sqrt{ab}$ I am not completely certain whether I am right and/or the triangle area trick is sufficient. $m>c'ab$ seems too high for anything more subtle like non-representability of $\min(a,b)-1$ initial integers. 22h comment Exact statistics in the Frobenius coin problem I think this works only if $m$ is sufficiently big right (say $\sqrt[i]{ab}$ at some $i\geq2$)? There seems more non-representable integers when $m$ is small (infact first consecutive $\min(a,b)-1$ non-zero integers are non-representable). 23h revised Exact statistics in the Frobenius coin problem edited tags 1d comment Probability distribution associated with total divisors of an integer I am looking something analogous to here en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93Kac_theorem (noting more sinister than this) 1d revised Probability distribution associated with total divisors of an integer edited tags 1d comment Exact statistics in the Frobenius coin problem @DouglasZare they are nor far apart $a=3$, $b=10^9$ not allowed. 1d revised Exact statistics in the Frobenius coin problem added 59 characters in body 1d revised Exact statistics in the Frobenius coin problem deleted 695 characters in body