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Abstract In this paper, we mainly prove the following conjectures of Sun 16: Let p > 3 be a prime. Then align* &A₂ A₂-16483p³B-₃\ (mod\ p⁴), \\ &A₂-₁ A₁+16p³3B-₃\ (mod\ p⁴), \\ &A₃ A₃-36738p³B-₃\ (mod\ p⁴), align* where Aₙ=₊=₀ⁿnk²n+kk² is the n th Apéry number, and B n is the n th Bernoulli number.
Mao et al. (Thu,) studied this question.