The Distribution of Squarefull Numbers in Short Intervals
نویسندگان
چکیده
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 between squarefull numbers is known. However, a better understanding of the distribution of squarefull numbers in short intervals can still be obtained. The result of Bateman and Grosswald easily implies that
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تاریخ انتشار 1994