Congruences involving generalized Catalan numbers and Bernoulli numbers

In this paper, we establish some congruences mod p3 involving the sums & sigma;p-1k=1 kmB2lp,k, where p > 3 is a prime number and Bp,k are generalized Catalan numbers. We also establish some congruences mod p2 involving the sums & sigma;p-1k=1 kmB2l1 p,kB2l2 p,k-d, where m, l1,l2, d are positive integers and 1 & LE;d & LE;p -1.

Automated summary

In this paper, we study some number theory problems by establishing congruences mod p3 involving the sums of one quadratic form and generalized Catalan numbers, as well as congruences mod p2 involving the sums of two quadratic forms and generalized Catalan numbers.