Show that there exists a set
of positive integers with the following property: for any infinite set
of primes, there exist two positive integers
in
and
not in
, each of which is a product of
distinct elements of
for some
.
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Show that there exists a set $A$ of positive integers with the following property: for any infinite set $S$ of primes, there exist two positive integers $m$ in $A$ and $n$ not in $A$, each of which is a product of $k$ distinct elements of $S$ for some $k \geq 2$.
Školjka