کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5772589 | 1630639 | 2017 | 9 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
New lower bounds for the least common multiple of polynomial sequences
ترجمه فارسی عنوان
مرزهای پایینی جدید برای چندین توالی چندجملهای توالی چندجملهای
دانلود مقاله + سفارش ترجمه
دانلود مقاله ISI انگلیسی
رایگان برای ایرانیان
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
چکیده انگلیسی
Let n be a positive integer and f(x) be a polynomial with nonnegative integer coefficients. We prove that lcmân/2ââ¤iâ¤n{f(i)}â¥2nâ1ân/2â for any positive integer n, where ân/2â denotes the smallest integer that is not less than n/2. This improves the lower bound obtained by Hong, Luo, Qian and Wang in 2013. For the least common multiple of the first n positive integers, we show that lcm1â¤iâ¤n{i}â¥2nâ3(nâ1)nâ22 for any integer nâ¥7, which improves the lower bound obtained by Nair in 1982 and by Farhi in 2009. For the least common multiple of consecutive quadratic progression terms, by using the integration method combined with a little more detailed analysis on the absolute value of complex numbers, we further show that lcmân/2ââ¤iâ¤n{ai2+c}â¥2nâ1ân/2ââ
minâ¡(a,ac) for any positive integer n, where a and c are two positive integers. This improves and extends the results obtained by Farhi in 2005 and Oon in 2013, respectively.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Number Theory - Volume 175, June 2017, Pages 191-199
Journal: Journal of Number Theory - Volume 175, June 2017, Pages 191-199
نویسندگان
Shaofang Hong, Guoyou Qian,