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Hans Publishers, Advances in Applied Mathematics, 3-5(49), p. 263-270

DOI: 10.1016/j.aam.2012.06.003

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Some q-congruences related to 3-adic valuations

Journal article published in 2009 by Hao Pan, Zhi-Wei Sun
This paper is available in a repository.
This paper is available in a repository.

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Red circle
Preprint: archiving forbidden
Red circle
Postprint: archiving forbidden
Red circle
Published version: archiving forbidden
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Abstract

In 1992, N. Strauss, J. Shallit and D. Zagier [Solution 6625, Am. Math. Mon. 99, No. 1, 66–69 (1992), http://www.jstor.org/stable/2324560] proved that for any positive integer a, ∑ k=0 3 a -1 2k k≡0(mod3 2a ) and furthermore 1 3 2a ∑ k=0 3 a -1 2k k≡1(mod3)· Recently a q-analogue of the first congruence was conjectured by V. J. W. Guo and J. Zeng [Adv. Appl. Math. 45, No. 3, 303–316 (2010; Zbl 1231.11020)]. In this paper we prove the conjecture of Guo and Zeng, and also give a q-analogue of the second congruence.