کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4593193 1630645 2016 14 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On quotients of values of Euler's function on the Catalan numbers
ترجمه فارسی عنوان
بر روی مقادیر عملکرد اویلر در اعداد کاتالان
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
چکیده انگلیسی

In a recent work, Luca and Stănică examined quotients of the form φ(Cm)φ(Cn), where φ   is Euler's totient function and C0,C1,C2…C0,C1,C2… is the sequence of the Catalan numbers. They observed that the number 4 (and analogously 14) appears noticeably often as a value of these quotients. We give an explanation of this phenomenon, based on Dickson's conjecture. It turns out not only that the value 4 is (in a certain sense) special in relation to the quotients φ(Cn+1)φ(Cn), but also that the value 4k4k has similar “special” properties with respect to the quotients φ(Cn+k)φ(Cn), and in particular we show that Dickson's conjecture implies that, for each k  , the number 4k4k appears infinitely often as a value of the quotients φ(Cn+k)φ(Cn).

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Number Theory - Volume 169, December 2016, Pages 160–173
نویسندگان
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