Answer by Ross Millikan for The number of (at most) $n-1$ distinct integers...
$p^{n-1}$ is a reasonable approximation which is accurate as long as $n \ll p$. The correct value is ${p \choose n-1}=p(p-1)(p-2)\ldots (p-n+2)$. Having chosen the acceptable values for the $x_j$s,...
View ArticleThe number of (at most) $n-1$ distinct integers $1\le x_1,\dots,x_k\le p$ is...
Let $k>n\ge1$ be integers.I have to estimate the number of choices for the numbers $x_1,\dots,x_k$, supposing that $1\le x_j\le p$, for an integer $p$ and that there are at most $n-1$ distinct...
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