We prove three more general supercongruences between truncated hypergeometric series and p-adic gamma function from which some known supercongruences follow. A supercongruence conjectured by Rodriguez--Villegas and proved by E. Mortenson using the theory of finite field hypergeometric series follows from one of our more general supercongruences. We also prove a supercongruence for 7F6 truncated hypergeometric series which is similar to a supercongruence proved by L. Long and R. Ramakrishna.

中文翻译：

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截断超几何级数和 p-adic 伽马函数的超同余

我们证明了截断的超几何级数和p-adic gamma 函数，一些已知的超同余函数由此而来。由 Rodriguez-Villegas 推测并由 E. Mortenson 使用有限域超几何级数理论证明的超同余来自我们更一般的超同余之一。我们还证明了一个超同余7F6截断的超几何级数，类似于 L. Long 和 R. Ramakrishna 证明的超同余。