Abstract
Pillai and Brauer proved that form≧17 we can find blocksB m ofm consecutive integers such that no element in the block is pairwise prime with each of the other elements. The following basic generalization is proved: For eachd>1 there is a numberG(d) such that for everym≧G(d) there exist infinitely many blocksB m ofm consecutive integers, such that for eachr∈B m there existss∈B m , (r,s)≧d.
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References
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Caro, Y. On a division property of consecutive integers. Israel J. Math. 33, 32–36 (1979). https://doi.org/10.1007/BF02760530
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DOI: https://doi.org/10.1007/BF02760530