Number Theory


The Connection Between X^2+1 and Balancing Numbers

Authors: Kelly Harris

Balancing numbers as introduced by Behera and Panda [1] can be shown to be connected to the formula x^2+1=N in a very simple way. The goal of this paper is to show that if a balancing number exists for the balancing equation 1+ 2+ ... + (y-1) = (y+1)+(y+2)+...+(y+m), then there is a corresponding(2y)^2+1=N, where N is composite. We will also show how this can be used to factor N.

Comments: 4 Pages.

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Submission history

[v1] 2019-12-31 01:10:18

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