On squares in polynomial products

Javier Cilleruelo; Florian Luca; Adolfo Quirós; Igor E. Shparlinski

doi:10.1007/s00605-008-0066-y

On squares in polynomial products

Javier Cilleruelo, Florian Luca^*, Adolfo Quirós, Igor E. Shparlinski

^*Corresponding author for this work

School of Computing

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

Let f(X) ∈ ℤ[X] be an irreducible polynomial of degree D ≥ 2 and let N be a sufficiently large positive integer. We estimate the number of positive integers n ≤ N such that the product is a perfect square. We also consider more general questions and give a lower bound on the number of distinct quadratic fields of the form ℚ(√F (n)), n = M + 1, ..., M + N.

Original language	English
Pages (from-to)	215-223
Number of pages	9
Journal	Monatshefte fur Mathematik
Volume	159
Issue number	3
DOIs	https://doi.org/10.1007/s00605-008-0066-y
Publication status	Published - Jan 2010

Access to Document

10.1007/s00605-008-0066-y

Cite this

@article{965a462c8b57487682d4a3250f4ac3dd,

title = "On squares in polynomial products",

abstract = "Let f(X) ∈ ℤ[X] be an irreducible polynomial of degree D ≥ 2 and let N be a sufficiently large positive integer. We estimate the number of positive integers n ≤ N such that the product is a perfect square. We also consider more general questions and give a lower bound on the number of distinct quadratic fields of the form ℚ(√F (n)), n = M + 1, ..., M + N.",

author = "Javier Cilleruelo and Florian Luca and Adolfo Quir{\'o}s and Shparlinski, \{Igor E.\}",

year = "2010",

month = jan,

doi = "10.1007/s00605-008-0066-y",

language = "English",

volume = "159",

pages = "215--223",

journal = "Monatshefte fur Mathematik",

issn = "0026-9255",

publisher = "Springer, Springer Nature",

number = "3",

}

TY - JOUR

T1 - On squares in polynomial products

AU - Cilleruelo, Javier

AU - Luca, Florian

AU - Quirós, Adolfo

AU - Shparlinski, Igor E.

PY - 2010/1

Y1 - 2010/1

N2 - Let f(X) ∈ ℤ[X] be an irreducible polynomial of degree D ≥ 2 and let N be a sufficiently large positive integer. We estimate the number of positive integers n ≤ N such that the product is a perfect square. We also consider more general questions and give a lower bound on the number of distinct quadratic fields of the form ℚ(√F (n)), n = M + 1, ..., M + N.

AB - Let f(X) ∈ ℤ[X] be an irreducible polynomial of degree D ≥ 2 and let N be a sufficiently large positive integer. We estimate the number of positive integers n ≤ N such that the product is a perfect square. We also consider more general questions and give a lower bound on the number of distinct quadratic fields of the form ℚ(√F (n)), n = M + 1, ..., M + N.

UR - https://www.scopus.com/pages/publications/75549091060

U2 - 10.1007/s00605-008-0066-y

DO - 10.1007/s00605-008-0066-y

M3 - Article

AN - SCOPUS:75549091060

SN - 0026-9255

VL - 159

SP - 215

EP - 223

JO - Monatshefte fur Mathematik

JF - Monatshefte fur Mathematik

IS - 3

ER -

On squares in polynomial products

Abstract

Access to Document

Other files and links

Fingerprint

Cite this