Finding almost squares
نویسندگان
چکیده
منابع مشابه
Finding Almost Squares
We study short intervals which contain an " almost square " , an integer n that can be factored as n = ab with a, b close to √ n. This is related to the problem on distribution of n 2 α (mod 1) and the problem on gaps between sums of two squares.
متن کامل2 INTEGERS 9 Supplement ( 2009 ) FINDING ALMOST SQUARES III
An almost square of type 2 is an integer n that can be factored in two different ways as n = a1b1 = a2b2 with a1, a2, b1, b2 ≈ √ n. In this paper, we shall improve upon our previous results on short intervals containing such an almost square. This leads to another question of independent interest: given some 0 < c < 1, find a short interval around x which contains an integer divisible by some i...
متن کاملThree Consecutive Almost Squares
Given a positive integer n, we let sfp(n) denote the squarefree part of n. We determine all positive integers n for which max{sfp(n), sfp(n+ 1), sfp(n+ 2)} ≤ 150 by relating the problem to finding integral points on elliptic curves. We also prove that there are infinitely many n for which max{sfp(n), sfp(n + 1), sfp(n + 2)} < n.
متن کاملFinding Almost-Perfect Graph Bisections
We give a polynomial time algorithm that given a graph which admits a bisection cutting a fraction (1 − ε) of edges, finds a bisection cutting a (1 − g(ε)) fraction of edges where g(ε) → 0 as ε→ 0. One can take g(ε) = O( 3 √ ε log(1/ε)). Previously known algorithms for Max Bisection could only guarantee finding a bisection that cuts a fraction of edges bounded away from 1 (in fact less than 3/4...
متن کاملAlgorithms for Finding Almost Irreducible and Almost Primitive Trinomials
Consider polynomials over GF(2). We describe efficient algorithms for finding trinomials with large irreducible (and possibly primitive) factors, and give examples of trinomials having a primitive factor of degree r for all Mersenne exponents r = ±3 mod 8 in the range 5 < r < 10, although there is no irreducible trinomial of degree r. We also give trinomials with a primitive factor of degree r ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 2006
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa121-3-2