Shorey, T. N.
(1986)
*Perfect powers in values of certain polynomials at integer points*
Mathematical Proceedings of the Cambridge Philosophical Society, 99
(2).
pp. 195-207.
ISSN 0305-0041

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Official URL: http://journals.cambridge.org/action/displayAbstra...

Related URL: http://dx.doi.org/10.1017/S0305004100064112

## Abstract

1. For an integer v > 1, we define P(v) to be the greatest prime factor of v and we write P(1) = 1. Let m ≥ 0 and k ≥ 2 be integers. Let d_{1}, ..., d_{t} with t ≥ 2 be distinct integers in the interval [1, k]. For integers l ≥ 2, y > 0 and b > 0 with P(b) ≤ k, we consider the equation (m+d_{1})...(m+d_{t})=by^{1}. (1) Put v1=1/2(1+1/l−2), l=4,5,... so that ½ < vt ≤ ¾. If α > 1 and kα < m ≤ kl, then equation (1) implies that P(m+d_{i})≤k for 1 ≤ i ≤ t and hence t<α^{-1}k+π(k).

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ID Code: | 67759 |

Deposited On: | 31 Oct 2011 13:23 |

Last Modified: | 31 Oct 2011 13:23 |

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