This paper provides a survey of results on the greatest prime factor, the number of distinct prime factors, the greatest squarefree factor and the greatest m-th powerfree part of a block of consecutive integers, both without any assumption and under assumption of the abc-conjecture. Finally we prove that the explicit abc-conjecture implies the Erd\H{o}s-Woods conjecture for each k>2.
CITATION STYLE
Shorey, T. N., & Tijdeman, R. (2016). Arithmetic Properties of Blocks of Consecutive Integers. In From Arithmetic to Zeta-Functions (pp. 455–471). Springer International Publishing. https://doi.org/10.1007/978-3-319-28203-9_27
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