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August 18th, 2010, 11:08 PM   #1
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integers

Suppose a1, a2, a3, a4, a5, a6, a7, a8 are eight distinct integers from {1,2...,16,17}. Show that there is an integer k>0 so that there are at least 3 different (not necessarily disjoint) pairs i and j so that ai - aj = k
Also find a set of seven distinct integers {1,2,...16,17} such that there in no integer k > 0 with that property.
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