Journal of Integer Sequences, Vol. 18 (2015), Article 15.8.6

Representation of Integers Using a2 + b2dc2

Peter Cho-Ho Lam
Department of Mathematics
Simon Fraser University
Burnaby, BC V5A1S6


A positive integer d is called special if every integer m can be expressed as a2 + b2dc2 for some nonzero integers a,b,c. A necessary condition for special numbers was recently given by Nowicki, and in this paper we prove its sufficiency. Thus, we give a complete characterization for special numbers.

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Received July 14 2015; revised version received July 29 2015. Published in Journal of Integer Sequences, July 29 2015.

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