Resumen de Power-partible reduction and congruences for Schröder polynomials

Chen Bo Jia, Rong-Hua Wang, Michael X. X. Zhong

• In this paper, we apply the power-partible reduction to show the following arithmetic properties of large Schröder polynomials Sn(z) and little Schröder polynomials sn(z): for any odd prime p, nonnegative integer r ∈ N, ε ∈ {−1, 1} and z ∈ Z with gcd(p,z(z + 1)) = 1, we have p−1 k=0 (2k + 1) 2r+1εk Sk (z) ≡ 1 (mod p) and p−1 k=0 (2k + 1) 2r+1εk sk (z) ≡ 0 (mod p)