The Product of Consecutive Integers Is Never a Power By

@inproceedings{Erds2004ThePO,
  title={The Product of Consecutive Integers Is Never a Power By},
  author={Paul Erdős and J. L. Selfridge},
  year={2004}
}
has no solution in integers with k >_ 2, 1 >_ 2 and n >_ 0 . (These restrictions on k, 1 and n will be implicit throughout this paper .) The early literature on this subject can be found in Dickson's history and the somewhat later literature in the paper of Obláth [5] . Rigge [6], and a few months later Erdös [1], proved the conjecture for 1 = 2 . Later these two authors [1] proved that for fixed 1 there are at most finitely many solutions to (1) . In 1940, Erdös and Siegel jointly proved that… CONTINUE READING
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