Anoteonthecongruenceswithsumsofpowersoftrinomial coefficients

Trinomial coefficientsn k 2 are defined byLet p > 3 be a prime number and n, m be positive integers, we obtained the congruences modulo p 2 with partial sums of powers of trinomial coefficientsWe also studied the congruences modulo p 2 with sums of powers of trinomial coefficients p-1 k=0 np -1 k m 2 and p-1 2 k=0 np -1 k m 2 .