SOME q-CONGRUENCES RELATED TO 3-ADIC VALUATIONS
نویسندگان
چکیده
In 1992, Strauss, Shallit and Zagier proved that for any positive integer a, 3−1 ∑ k=0 (2k k ) ≡ 0 (mod 3) and furthermore 1 32a 3−1 ∑ k=0 (2k k ) ≡ 1(mod 3). Recently a q-analogue of the first congruence was conjectured by Guo and Zeng. In this paper we prove the conjecture of Guo and Zeng, and also give a q-analogue of the second congruence.
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