2015 USAMO Problems/Problem 6
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Problem 6
Consider , and let
be a multiset of positive integers. Let
. Assume that for every
, the set
contains at most
numbers. Show that there are infinitely many
for which the sum of the elements in
is at most
. (A multiset is a set-like collection of elements in which order is ignored, but repetition of elements is allowed and multiplicity of elements is significant. For example, multisets
and
are equivalent, but
and
differ.)