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Diophantine equations of Erdös-Moser type

Published online by Cambridge University Press:  17 April 2009

Pieter Moree
Pieter Moree
Affiliation:
Department of MathematicsMacquarie UniversitySydney NSW 2109Australia
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Abstract

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Using an old result of Von Staudt on sums of consecutive integer powers, we shall show by an elementary method that the Diophantine equation 1k + 2k + … + (x − l)k = axk has no solutions (a, x, k) with k > 1, . For a = 1 this equation reduces to the Erdös-Moser equation and the result to a result of Moser. Our method can also be used to deal with variants of the equation of the title, and two examples will be given. For one of them there are no integer solutions with

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 53 , Issue 2 , April 1996 , pp. 281 - 292
Copyright
Copyright © Australian Mathematical Society 1996

References

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