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Original Articles

The p-adic Valuation of Eulerian Numbers: Trees and Bernoulli Numbers

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REFERENCES

  • [Amdeberhan et al. 08] T. Amdeberhan, D. Manna, and V. Moll. “The 2-adic Valuation of Stirling Numbers.” Experimental Mathematics 17 (2008), 69–82.
  • [Amdeberhan et al. 09] T. Amdeberhan, V. Moll, and A. Straub. “The p-adic Valuation of k-Central Binomial Coefficients.” Acta Arithmetica 149 (2009), 31–42.
  • [Berrizbeitia et al. 10] A. Berrizbeitia, L. A. Medina, A. Moll, V. Moll, and L. Noble. “The p-adic Valuation of Stirling Numbers.” Journal for Algebra and Number Theory Academia 1 (2010), 1–30.
  • [Carlitz and Riordan 53] L. Carlitz and J. Riordan. “Congruences for Eulerian Numbers.” Duke Math. J. 20 (1953), 339–343.
  • [Glaisher 01] J. W. L. Glaisher. “On the Residues of the Sums of the Inverse Powers of Numbers in Arithmetical Progression.” Q. J. Math. 32 (1901), 271–288.
  • [Jensen 15] K. L. Jensen. “Om talteoretiske Egenskaber ved de Bernoulliske Tal.” Nyt Tidsskr. Mat. B 26 (1915), 73–83.
  • [Koblitz 96] Neal Koblitz. p-adic Numbers, p-adic Analysis, and Zeta-Functions, 2nd edition. Springer, 1996.
  • [Lehmer 38] E. Lehmer. “On Congruences Involving Bernoulli Numbers and Quotients of Fermat and Wilson.” Ann. Math. 39 (1938), 350–360.
  • [Lengyel 95] T. Lengyel. “The Order of the Fibonacci and Lucas Numbers.” The Fibonacci Quarterly 33 (1995), 234–239.
  • [Lengyel 09] T. Lengyel. “On the 2-adic Order of Stirling Numbers of the Second Kind and Their Differences.” DMTCS Proc. AK (2009), 561–572.
  • [McIntosh and Roettger 07] R. J. McIntosh and E. L. Roettger. “A search for Fibonacci–Wieferich and Wolstenholme Primes.” Math. Comp. 76 (2007), 2087–2094.
  • [Ribenboim 79] P. Ribenboim. 13 Lectures on Fermat’s Last Theorem. Springer, 1979.
  • [Wall 60] D. D. Wall. “Fibonacci Series modulo m.” Amer. Math. Monthly 67 (1960), 525–532.
  • [Zhao et al. 14a] J. Zhao, S. Hong, and W. Zhao. “Divisibility by 2 of Stirling Numbers of the Second Kind and Their Differences.” Journal of Number Theory 140 (2014), 324–348.
  • [Zhao et al. 14b] W. Zhao, J. Zhao, and S. Hong. “The 2-adic Valuations Of Differences of Stirling Numbers of the Second Kind.” Unpublished manuscript, August2014.

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