کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
9515468 1343457 2005 13 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Shifted products that are coprime pure powers
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات گسسته و ترکیبات
پیش نمایش صفحه اول مقاله
Shifted products that are coprime pure powers
چکیده انگلیسی
A set A of positive integers is called a coprime Diophantine powerset if the shifted product ab+1 of two different elements a and b of A is always a pure power, and the occurring pure powers are all coprime. We prove that each coprime Diophantine powerset A⊂{1,…,N} has |A|⩽8000logN/loglogN for sufficiently large N. The proof combines results from extremal graph theory with number theory. Assuming the famous abc-conjecture, we are able to both drop the coprimality condition and reduce the upper bound to cloglogN for a fixed constant c.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Combinatorial Theory, Series A - Volume 111, Issue 1, July 2005, Pages 24-36
نویسندگان
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