Supercongruences on some binomial sums involving Lucas sequences

In this paper, we confirm several conjectured congruences of Sun concerning the divisibility of binomial sums. For example, with help of a quadratic hypergeometric transformation, we prove that∑k=0p−1(p−1k)(2kk)2Pk8k≡0(modp2) for any prime p≡7(mod8), where Pk is the k-th Pell number. Further, we also propose three new congruences of the same type.