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Chebyshev polynomials of the first kind and primality testing

Home Page: https://mathoverflow.net/questions/286626/is-there-an-explicit-expression-for-chebyshev-polynomials-modulo-xr-1/286639#286639

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Chebyshev polynomials of the first kind and primality testing

Conjecture 41

Let n be a natural number greater than two . Let r be the smallest odd prime number such that r \nmid n and n^2 \not\equiv 1 \pmod r . Let T_n(x) be Chebyshev polynomial of the first kind , then n is a prime number if and only if T_n(x) \equiv x^n \pmod {x^r-1,n} .

See Chebyshev polynomials of the first kind and primality testing and Conjecture 41 of Peđa Terzić.

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2021, Olexa Bilaniuk & Dendi Suhubdy

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