Proof of some conjectural congruences involving Apéry and Apéry-like numbers
Proof of some conjectural congruences involving Apéry and Apéry-like numbers
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Cambridge, UK: Cambridge University Press
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English
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Cambridge, UK: Cambridge University Press
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In this paper, we mainly prove the following conjectures of Sun [16]: Let p > 3 be a prime. Then
\begin{align*}
&A_{2p}\equiv A_2-\frac{1648}3p^3B_{p-3}\ ({\rm{mod}}\ p^4),\\
&A_{2p-1}\equiv A_1+\frac{16p^3}3B_{p-3}\ ({\rm{mod}}\ p^4),\\
&A_{3p}\equiv A_3-36738p^3B_{p-3}\ ({\rm{mod}}\ p^4),
\end{align*} where $A_n=\sum_{k=0}^n\binom{...
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Proof of some conjectural congruences involving Apéry and Apéry-like numbers
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TN_cdi_proquest_journals_3055291033
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https://devfeature-collection.sl.nsw.gov.au/record/TN_cdi_proquest_journals_3055291033
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ISSN
0013-0915
E-ISSN
1464-3839
DOI
10.1017/S0013091524000075
