Some Congruence Properties of Stirling Numbers of the Second Kind
Authors
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Department of Mathematics, Government Champhai College Champhai - 796 321, Mizoram ,IN
A. Lalchhuangliana -
Department of Maths. and Comp. Sc., Mizoram University, Aizawl Aizawl - 796 004, Mizoram ,INS. S. Singh
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Department of Mathematics, Guru Nanak Dev University, Amritsar - 143 005, Punjab ,INJitender Singh
DOI:
https://doi.org/10.18311/jims/2024/30253Keywords:
Congruence, divisibility, primes, p-adic valuation, Stirling numbersAbstract
This paper establishes certain formulas for p-adic valuation of Stirling numbers of the second kind S(pn, k) where p is a prime and some related classes. The parity of k also affects the p-adic valuation of S(n, k) if k is divisible by p. In fact, vp(S(p2, kp)) ≥ 5 if k is even. The congruence properties of S(pn, k) (mod p2) depend on the sum of the p-adic digits of k when k is not a multiple of p.
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Copyright (c) 2024 A. Lalchhuangliana, S. S. Singh, Jitender Singh
This work is licensed under a Creative Commons Attribution 4.0 International License.
Accepted 2022-11-07
Published 2024-01-01
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