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
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Some divisibility properties of binomial and q-binomial coefficients
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
نویسندگان
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