Three consecutive almost squares

Jeremy Rouse; Yilin Yang

doi:10.1142/S1793042116500603

Three consecutive almost squares

Jeremy Rouse, Yilin Yang

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

Abstract

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)} < n1/3. © 2016 World Scientific Publishing Company.

Original language	English
Pages (from-to)	969-978
Journal	International Journal of Number Theory
Volume	12
Issue number	4
DOIs	https://doi.org/10.1142/S1793042116500603
Publication status	Published - 1 Jun 2016
Externally published	Yes

Bibliographical note

Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

Research Keywords

Elliptic curves
Heegner points
Pell equation

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title = "Three consecutive almost squares",

abstract = "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)} < n1/3. {\textcopyright} 2016 World Scientific Publishing Company.",

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AU - Yang, Yilin

N1 - Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

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N2 - 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)} < n1/3. © 2016 World Scientific Publishing Company.

AB - 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)} < n1/3. © 2016 World Scientific Publishing Company.

KW - Elliptic curves

KW - Heegner points

KW - Pell equation

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DO - 10.1142/S1793042116500603

M3 - RGC 21 - Publication in refereed journal

SN - 1793-0421

VL - 12

SP - 969

EP - 978

JO - International Journal of Number Theory

JF - International Journal of Number Theory

IS - 4

ER -

Three consecutive almost squares

Abstract

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Research Keywords

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