Geodesic
On some properties of Chebyshev polynomials
Discussiones Mathematicae. General Algebra and Applications, Tome 28 (2008) no. 1, pp. 121-133.

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Letting T_n (resp. U_n) be the n-th Chebyshev polynomials of the first (resp. second) kind, we prove that the sequences (X^kT_n-k)_k and (X^kU_n-k)_k for n - 2⎣n/2⎦ ≤ k ≤ n - ⎣n/2⎦ are two basis of the ℚ-vectorial space _n[X] formed by the polynomials of ℚ[X] having the same parity as n and of degree ≤ n. Also T_n and U_n admit remarkableness integer coordinates on each of the two basis.
Keywords: Chebyshev polynomials, integer coordinates 
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Belbachir, Hacène; Bencherif, Farid. On some properties of Chebyshev polynomials. Discussiones Mathematicae. General Algebra and Applications, Tome 28 (2008) no. 1, pp. 121-133. http://geodesic.mathdoc.fr/item/DMGAA_2008_28_1_a6/

[1] H. Belbachir and F. Bencherif, Linear recurrent sequences and powers of a square matrix, Integers 6 (A12) (2006), 1-17.

[2] E. Lucas, Théorie des Nombres, Ghautier-Villars, Paris 1891.

[3] T.J. Rivlin, Chebyshev Polynomials: From Approximation Theory to Algebra and Number Theory, second edition, Wiley Interscience 1990.