On the equation P(x) = n! and a question of Erdős

Daniel Berend; Charles F. Osgood

doi:10.1016/0022-314X(92)90020-P

On the equation P(x) = n! and a question of Erdős

Daniel Berend, Charles F. Osgood

Department of Computer Science

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

Given a polynomial P of degree ≥ 2 with integer coefficients, it is shown that the set of n, for which the equation P(x) = n! has an integer solution x, is of density zero. This answers in particular a question of Erdo{combining double acute accent}s.

Original language	English
Pages (from-to)	189-193
Number of pages	5
Journal	Journal of Number Theory
Volume	42
Issue number	2
DOIs	https://doi.org/10.1016/0022-314X(92)90020-P
State	Published - 1 Jan 1992

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/0022-314X(92)90020-P

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title = "On the equation P(x) = n! and a question of Erd{\H o}s",

abstract = "Given a polynomial P of degree ≥ 2 with integer coefficients, it is shown that the set of n, for which the equation P(x) = n! has an integer solution x, is of density zero. This answers in particular a question of Erdo{combining double acute accent}s.",

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AU - Osgood, Charles F.

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N2 - Given a polynomial P of degree ≥ 2 with integer coefficients, it is shown that the set of n, for which the equation P(x) = n! has an integer solution x, is of density zero. This answers in particular a question of Erdo{combining double acute accent}s.

AB - Given a polynomial P of degree ≥ 2 with integer coefficients, it is shown that the set of n, for which the equation P(x) = n! has an integer solution x, is of density zero. This answers in particular a question of Erdo{combining double acute accent}s.

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U2 - 10.1016/0022-314X(92)90020-P

DO - 10.1016/0022-314X(92)90020-P

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On the equation P(x) = n! and a question of Erdős

Abstract

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