Square product of three integers in short intervals

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.

Products of integers in short intervals

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 ...

On 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...

Squarefree Integers without Large Prime Factors in Short Intervals

Integers without large prime factors in short intervals and arithmetic progressions