Let $n$ be a nonnegative integer. The $n$-th Ap\'{ e}ry number is defined by $$ A_n:=\sum_{ k=0}^n\binom{ n+k}{ k}^2\binom{ n}{ k}^2. $$ Z.-W. Sun ever investigated the congruence properties of Ap\'{ e}ry numbers and posed some conjectures. For example, Sun conjectured that for any prime $p\geq7$ $$ \sum_{ k=0}^{ p-1}(2k+1)A_k\equiv p-\frac{ 7}{ 2}p^2H_{ p-1}\pmod{ p^6} $$ and for any prime $p\geq5$ $$ \sum_{ k=0}^{ p-1}(2k+1)^3A_k\equiv p^3+4p^4H_{ p-1}+\frac{ 6}{ 5}p^8B_{ p-5}\pmod{ p^9}, $$ where $H_n=\sum_{ k=1}^n1/k$ denotes the $n$-th harmonic number and $B_0,B_1,\ldots$ are the well-known Bernoulli numbers. In this paper we shall confirm these two conjectures.
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