• 1 A Private Mathematics Academy

In this article, we extend Z. H. Sun's congruences concerning Legendre polynomials P p−1 2 (x) to P p+1 2 (x) for odd prime p, which enables us to deduce some congruences resembling p+1 2 ∑ k=0 4pk + 4k 2 − 1 16 k (2k − 1) 2 (2k k)2 (mod p 2).