# Relation of Boubaker Polynomials to Dickson Polynomials

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## Theorem

The Boubaker polynomials $B_n$ are linked to the Dickson polynomials by the relations:

- $\map {B_{n + 1} } x \map {B_{n + j} } x - \map {B_{n + j + 1} } x \map {B_n} x = \paren {3 x^2 + 4} \map {D_{n + 1} } {x, \dfrac 1 4}$

- $\map {B_n} x = \map {D_n} {2 x, \dfrac 1 4} + 4 \map {D_{n - 1} } {2 x, \dfrac 1 4}$

## Proof

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