کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4594052 | 1630679 | 2014 | 18 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Some divisibility properties of binomial and q-binomial coefficients
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
We first prove that if a has a prime factor not dividing b then there are infinitely many positive integers n such that (an+bnan) is not divisible by bn+1bn+1. This confirms a recent conjecture of Z.-W. Sun. Moreover, we provide some new divisibility properties of binomial coefficients: for example, we prove that (12n3n) and (12n4n) are divisible by 6n−16n−1, and that (330n88n) is divisible by 66n−166n−1, for all positive integers n. As we show, the latter results are in fact consequences of divisibility and positivity results for quotients of q-binomial coefficients by q-integers, generalising the positivity of q-Catalan numbers. We also put forward several related conjectures.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Number Theory - Volume 135, February 2014, Pages 167–184
Journal: Journal of Number Theory - Volume 135, February 2014, Pages 167–184
نویسندگان
Victor J.W. Guo, C. Krattenthaler,