Supercongruences involving binomial coefficients and Euler polynomials

Let p be an odd prime and let x be a p-adic integer. In this paper, we establish supercongruences for ₊=₀^p-1x{kx+kk (-4) ᵏ} (dk+1) 2k{k}p² and ₊=₀^p-1x{kx+kk (-2) ᵏ} (dk+1) 2k{k}p², where d\0, 1, 2\. As consequences, we extend some known results. For example, for p>3 we show ₊=₀^p-13kk (427) ᵏ19+89p+427pE₏-₂ (13) p², where Eₙ (x) denotes the Euler polynomial of degree n. This generalizes a known congruence of Z. -W. Sun.