کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6415556 1335727 2013 22 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A generalization of the Gaussian formula and a q-analog of Fleckʼs congruence
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
A generalization of the Gaussian formula and a q-analog of Fleckʼs congruence
چکیده انگلیسی

The q-binomial coefficients are the polynomial cousins of the traditional binomial coefficients, and a number of identities for binomial coefficients can be translated into this polynomial setting. For instance, the familiar vanishing of the alternating sum across row n∈Z+ of Pascalʼs triangle is captured by the so-called Gaussian formula, which states that ∑m=0n(−1)m(nm)q is 0 if n is odd, and is equal to ∏kodd(1−qk) if n is even. In this paper, we find a q-binomial congruence which synthesizes this result and Fleckʼs congruence for binomial coefficients, which asserts that for n,p∈Z+, with p a prime,∑m≡j(modp)(−1)m(nm)≡0(modp⌊n−1p−1⌋).

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Number Theory - Volume 133, Issue 11, November 2013, Pages 3717-3738
نویسندگان
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