Some supercongruences of arbitrary length

Frits Beukers (1) , Eric Delaygue (2)

1 Mathematical Institute
2 CTN - Combinatoire, théorie des nombres

We prove supercongruences modulo $p^2$ for values of truncated hypergeometric series at some special points. The parameters of the hypergeometric series are $d$ copies of $1/2$ and $d$ copies of $1$ for any integer $d\ge2$.

Domaines: Théorie des nombres [math.NT]

Frits Beukers, Eric Delaygue. Some supercongruences of arbitrary length. Indagationes Mathematicae, 2022, 33 (5), pp.946-955. ⟨10.1016/j.indag.2022.04.002⟩. ⟨hal-02091737⟩