On sets of integers whose shifted products are powers |
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| Authors: | C.L. Stewart |
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| Affiliation: | Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1 |
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| Abstract: | Let N be a positive integer and let A be a subset of {1,…,N} with the property that aa′+1 is a pure power whenever a and a′ are distinct elements of A. We prove that |A|, the cardinality of A, is not large. In particular, we show that |A|?(logN)2/3(loglogN)1/3. |
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| Keywords: | Pure powers Extremal graph theory Linear forms in logarithms |
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