Finding Almost Squares V

Tsz Ho Chan

doi:10.1515/integ.2010.046

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Finding Almost Squares V

Published/Copyright: November 5, 2010

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From the journal Volume 10 Issue 5

Abstract

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, . In this paper, we continue the study of almost squares of type 2 in short intervals and improve the 1/2 upper bound. We also draw connections with almost squares of type 1.

Keywords.: Almost squares; elementary method

Received: 2010-01-08

Accepted: 2010-05-14

Published Online: 2010-11-05

Published in Print: 2010-November

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Some Divisibility Properties of Binomial Coefficients and the Converse of Wolstenholme's Theorem
On the Iteration of a Function Related to Euler's φ-Function
An Explicit Evaluation of the Gosper Sum
On the Frobenius Problem for {a^k, a^k + 1, a^k + a, . . . , a^k + a^k⁻¹}
Generalizing the Combinatorics of Binomial Coefficients via -Nomials
Finding Almost Squares V
On Relatively Prime Subsets and Supersets
Reformed Permutations in Mousetrap and Its Generalizations
On Ternary Inclusion-Exclusion Polynomials
Sums and Products of Distinct Sets and Distinct Elements in ℂ

https://doi.org/10.1515/integ.2010.046

Keywords for this article

Almost squares; elementary method

Articles in the same Issue

Some Divisibility Properties of Binomial Coefficients and the Converse of Wolstenholme's Theorem
On the Iteration of a Function Related to Euler's φ-Function
An Explicit Evaluation of the Gosper Sum
On the Frobenius Problem for {a^k, a^k + 1, a^k + a, . . . , a^k + a^k⁻¹}
Generalizing the Combinatorics of Binomial Coefficients via -Nomials
Finding Almost Squares V
On Relatively Prime Subsets and Supersets
Reformed Permutations in Mousetrap and Its Generalizations
On Ternary Inclusion-Exclusion Polynomials
Sums and Products of Distinct Sets and Distinct Elements in ℂ