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Smooth Numbers in Short Intervals
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It follows that there is a positive constant c1 and arbitrarily large values of x for which the interval (x; x+ c1x ] contains no squarefull numbers. On the other hand, since there is a square in (x; x + 2 p x + 1] for all x 0, it follows that there is a constant c2 such that for every x 1, the interval (x; x + c2x] contains a squarefull number. Thus, the order of the maximum size of gaps betwe...
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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 2005
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972700037953