On a Supercongruence Conjecture of Z.-W. Sun

In this paper, the author partly proves a supercongruence conjectured by Z.-W. Sun in 2013. Let p be an odd prime and let a ∈ ℤ⁺. Then, if p ≡ 1 (mod 3)

$$sumlimits_{k = 0}^{leftlfloor {{5 over 6}{p^a}} rightrfloor } {{{left( {matrix{{2k} cr k cr } } right)} over {{{16}^k}}} equiv left( {{3 over {{p^a}}}} right),,left( {bmod ,{p^2}} right)} $$

is obtained, where (÷) is the Jacobi symbol.