Abstract
The q-Euler numbers and polynomials were recently constructed [T. Kim, “The Modified q-Euler Numbers and Polynomials,” Adv. Stud. Contemp. Math., 16, 161–170 (2008)]. These q-Euler numbers and polynomials have interesting properties. In this paper, we prove a theorem of the von Staudt-Clausen type for q-Euler numbers; namely, we prove that the q-Euler numbers are p-adic integers. Finally, we prove Kummer-type congruences for the q-Euler numbers.
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Kim, T. On the von Staudt-Clausen theorem for q-Euler numbers. Russ. J. Math. Phys. 20, 33–38 (2013). https://doi.org/10.1134/S1061920813010044
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DOI: https://doi.org/10.1134/S1061920813010044