Journal of Integer Sequences, Vol. 18 (2015), Article 15.2.3

The Numbers a2 + b2dc2

Andrzej Nowicki
Nicolaus Copernicus University
Faculty of Mathematics and Computer Science
87-100 Toruń


We say that a positive integer d is special if for every integer m there exist nonzero integers a, b, c such that m = a2 + b2dc2. In this note we present examples and some properties of special numbers. Moreover, we present an infinite sequence of special numbers.

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(Concerned with sequences A000217 A001110.)

Received November 18 2014; revised versions received December 16 2014; December 18 2014. Published in Journal of Integer Sequences, January 24 2015.

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