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On a Family of Diophantine Difference Equations
Author(s) -
Shiu P.
Publication year - 1996
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/28.4.343
Subject(s) - mathematics , diophantine equation , prime (order theory) , exponential function , prime number , pure mathematics , constant (computer programming) , diophantine set , discrete mathematics , combinatorics , mathematical analysis , computer science , programming language
The family of Diophantine difference equations considered by J. H. Conway, H. T. Croft, P. Erdős and M. J. T. Guy can be solved in closed form when the parameter is a prime. The associated characterisation problem is shown to be related to the determination of certain constants, which also happen to be coefficients in the asymptotic formula for the associated exponential sum.