How often can a given distance occur in a finite set of integers? |
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| Authors: | Egbert Harzheim |
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| Institution: | (1) Department of Mathematics, Lehman College (CUNY), Bronx, New York 10468, USA;(2) CUNY Graduate Center, New York, 10016, USA |
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| Abstract: | Let n, a, d be natural numbers and A a set of integers of the closed interval 0, n] with | A | = a. Then we establish sharp lower and upper bounds for the number of pairs (x,y) ? A×A(x,y)\in A\times A for which y - x = d. Roughly spoken, we investigate how often a distance d can occur in A. |
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