We show that, under reasonable assumptions, two negative roots can be eliminated from the characteristic equation of a polynomial-like iterative equation. This result gives a new case where we may lower the order of such an equation.
We use the recurrence relations and the Pell equations to determineall integer triangles whose lengths are consecutive integers and the length ofa fixed median is a rational number.
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Some aspects of duality triads introduced recently are discussed. In particular, the general solution for the triad polynomials is given. Furthermore, a generalization of the notion of duality triad is proposed and some simple properties of these generalized duality triads are derived.
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It is shown that duality triads of higher rank are closely related to orthogonal matrix polynomials on the real line. Furthermore, some examples of duality triads of higher rank are discussed. In particular, it is shown that the generalized Stirling numbers of rank r give rise to a duality triad of rank r.
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