Representation of Integers Using
a2 + b2 − dc2
Peter Cho-Ho Lam
Department of Mathematics
Simon Fraser University
Burnaby, BC V5A1S6
Canada
Abstract:
A positive integer d is called special if every integer m
can be expressed as
a2 + b2 − dc2
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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