Number Theory

A Sum of Three Squares in Which One is the Product of the Other Two

Authors: Walter A. Kehowski
Comments: 10 Pages.

The identity x^2 + (x+1)^2 + (x(x+1))^2 = (x^2+x+1)^2 is the motivation for study of the equation d^2 + e^2 + n^2 = x^2, where d and e are conjugate divisors of n, that is, n=de and $d1 fall empirically into two families: a triangular family mathscr{T}, and a Fibonacci family mathscr{F}, with virtually no overlap. It is conjectured that the two families comprise all n with |N_{n}|>1.
Category: Number Theory