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.
2021, Olexa Bilaniuk & Dendi Suhubdy