We prove some supercongruences involving the Apéry polynomials
the generalized Domb numbers
which were conjectured by Z.-W. Sun. For example, we show that for any prime and positive integer we have
where are the Bernoulli numbers. The following supercongruences hold modulo :
where denotes the Legendre symbol and are the Euler numbers.
"Some conjectural supercongruences related to Bernoulli and Euler numbers." Rocky Mountain J. Math. 52 (3) 1105 - 1126, June 2022. https://doi.org/10.1216/rmj.2022.52.1105