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ON PRIMES AND POWERS OF A FIXED INTEGER

Published online by Cambridge University Press:  24 March 2003

P. D. T. A. ELLIOTT
P. D. T. A. ELLIOTT
Affiliation:
Department of Mathematics, University of Colorado, Boulder, CO 80309-0395, USApdtae@euclid.colorado.edu
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Abstract

According to a 1904 conjecture of Dickson [2] unless prevented by congruence conditions, any finite collection of linear forms in $\Z[x]$ with positive leading coefficients infinitely often simultaneously represent primes. For the forms $x,x+2$ this includes the conjectured infinitude of prime-pairs.

Keywords

11N0511D8511N25
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 67 , Issue 2 , April 2003 , pp. 365 - 379
Copyright
The London Mathematical Society 2003

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