2 problems

Let $T_k(b,c)$ denote the generalized central trinomial coefficient. For an odd prime $p$, let $\left(\frac{a}{p}\right)$ be the Legendre symbol. Sun's conjecture. … If $p>3$, then…

Let $T_n$ be the coefficient of $x^n$ in the expansion of $(x^2+x+1)^n$. Sun's supercongruence conjecture. For any prime $p>3$ and positive integer $n$, the quotient … is a $p$-adi…