Given a set of positive integers with no collisions (that is, every element is unique), $A = \{\ldots\}$, how can I find the smallest modulus, $n$, so that $B = A \pmod n$ has no collisions?
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We may just consider the difference set $D=A-A$, then take the least positive integer $n$ such that $n$ does not divide any positive element of $D$. Such $n$ is obviously a prime number.
Jack D'Aurizio
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2Do you really mean $D=A-A=\emptyset$? – Mårten W Oct 30 '15 at 23:56
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2@MårtenW: the difference set $A-A$ is defined as $$A-A = {a-b:a,b\in A}.$$ – Jack D'Aurizio Oct 31 '15 at 13:41