A Proof of a Conjecture of Zhi-Wei Sun on a Truncated Legendre-Symbol Determinant

Yaoran Yang, Gaishi Yang, Yutong Zhang

We prove Conjecture~3.4 of Zhi-Wei Sun by evaluating, for every prime $p\equiv 3(\mathrm{mod}4)$, a truncated Legendre-symbol determinant as $\lfloor (p-2)/3{\rfloor }^{2}x$. The argument reduce…