Abstract
We describe a decomposition of the polynomials f n := f n,B,a defined by $$f_{0}:=B,\quad f_{1}(x):=x,\quad f_{n+1}(x) = xf_{n}(x) -af_{n-1}(x)$$ where B and a are rational numbers. We also present an application to related Diophantine equations.
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