Chebyshev Polynomials and Primality Tests
نویسندگان
چکیده
Algebraic properties of Chebyshev polynomials are presented. The complete factorization of Chebyshev polynomials of the rst kind (Tn(x)) and second kind (Un(x)) over the integers are linked directly to divisors of n and n + 1 respectively. For any odd integer n, it is shown that the polynomial Tn(x)=x is irreducible over the integers i n is prime. The result leads to a generalization of Fermat's little theorem and an e ective test for the compositeness of an integer. Also, factoring of integers is linked directly to the construction of a related Chebyshev polynomial.
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