A family of super congruences involving multiple harmonic sums
In recent years, the congruence ∑i+j+k=pi,j,k>01ijk≡−2Bp−3(mod p), first discovered by the last author has been generalized by either increasing the number of indices and considering the corresponding super congruences, or by considering the alternating version of multiple harmonic sums. In t...
| Hlavní autoři: | , , , |
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| Médium: | Journal article |
| Jazyk: | English |
| Vydáno: |
World Scientific Publishing
2016
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| Shrnutí: | In recent years, the congruence ∑i+j+k=pi,j,k>01ijk≡−2Bp−3(mod p), first discovered by the last author has been generalized by either increasing the number of indices and considering the corresponding super congruences, or by considering the alternating version of multiple harmonic sums. In this paper, we prove a family of similar super congruences modulo prime powers pr with the indices summing up to mpr where m is coprime to p, and where all the indices are also coprime to p. |
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