Congruences involving Bernoulli and Euler numbers

Let [x][x] be the integral part of x  . Let p>5p>5 be a prime. In the paper we mainly determine ∑x=1[p/4]1xk(modp2), (p−1)(modp3), ∑k=1p−12kk(modp3) and ∑k=1p−12kk2(modp2) in terms of Euler and Bernoulli numbers. For example, we have∑x=1[p/4]1x2≡(−1)p−12(8Ep−3−4E2p−4)+143pBp−3(modp2), where EnEn is the n  th Euler number and BnBn is the nth Bernoulli number.