PRIMALITY FROM FACTORIZATION PROPERTIES OF CHEBYSHEV POLYNOMIALS
Let be the nth Chebyshev polynomial of the first kind and let be the th Chebyshev polynomial of the second kind. In this paper we investigate relationships between the primality of an integer n and factorization properties of and characterizing prime numbers in terms of these polynomials. Examples of these characterizations include (i) an odd integer n is prime if and only if is irreducible over the integers and (ii) an odd integer n is prime if and only if We also show that and have exactly two irreducible factors when and only when n is an odd prime.
primality, Chebyshev polynomial.