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Perfect powers in values of certain polynomials at integer points

Published online by Cambridge University Press:  24 October 2008

T. N. Shorey
T. N. Shorey
Affiliation:
School of Mathematics, Tata Institute of Fundamental Research, Bombay 400005, India
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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 d1, …, dt 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

Put

so that ½ < vt ≤ ¾. If α > 1 and kα < m ≤ kl, then equation (1) implies that

for 1 ≤ i ≤ t and hence

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 99 , Issue 2 , March 1986 , pp. 195 - 207
Copyright
Copyright © Cambridge Philosophical Society 1986

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References

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