Products of integers in short intervals
نویسنده
چکیده
1 . Introduction . In this paper we discuss various properties distinct integers n 1 , . . ., of taken from a short interval may have, such as f H n, e N"` for some m cN, m > 2 : the product of n l , . . ., of is a perfect i=1 power ; 11 n. _ fl n, for distinct subsets l i , 12 of ; l, . . ., f ; : there exist two icl I iEl ) distinct subsets of (n 1 , . . ., nf , that yield the same result if their elements are multiplied ;
منابع مشابه
Square product of three integers in short intervals
In this paper we list all the integer triplets taken from an interval of length ≤ 12, whose products are perfect squares.
متن کاملیکپارچه سازی برنامهریزی و زمانبندی تولید در صنایع فرآیندی چند محصولی با سیستم تولیدی پیوسته
One of the main elements of each supply chain is production. Production planning in multi-products process industries in which products are subjected to the complicated operational constraints is a very hard work because production of computed optimal volume should be compatible with operation scheduling constraints of production system. Thus, integration idea has been proposed for required d...
متن کاملDistribution of Inverses and Multiples of Small Integers and the Sato–Tate Conjecture on Average
We show that, for sufficiently large integers m and X, for almost all a = 1,. .. , m the ratios a/x and the products ax, where |x| X, are very uniformly distributed in the residue ring modulo m. This extends some recent results of Garaev and Karatsuba. We apply this result to show that on average over r and s, ranging over relatively short intervals, the distribution of Kloosterman sums K r,s (...
متن کاملDistribution of Modular Inverses and Multiples of Small Integers and the Sato–Tate Conjecture on Average
We show that, for sufficiently large integers m and X, for almost all a = 1,. .. , m the ratios a/x and the products ax, where |x| X, are very uniformly distributed in the residue ring modulo m. This extends some recent results of Garaev and Karatsuba. We apply this result to show that on average over r and s, ranging over relatively short intervals, the distribution of Kloosterman sums K r,s (...
متن کاملOn algebraic integers in short intervals and near smooth curves
In 1970 A. Baker and W. Schmidt introduced the concept of a regular system of numbers and vectors. They proved that the set of real algebraic numbers forms a regular system on any fixed interval. This fact has allowed to prove some important results in the metric theory of transcendental numbers. In this paper their approach is applied to the set of algebraic integers α in short intervals of le...
متن کامل