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 - http://www.scopus.com/inward/record.url?scp=75549091060&partnerID=8YFLogxK

U2 - 10.1007/s00605-008-0066-y

DO - 10.1007/s00605-008-0066-y

M3 - Article

VL - 159

SP - 215

EP - 223

JO - Monatshefte fur Mathematik

JF - Monatshefte fur Mathematik

SN - 0026-9255

IS - 3

ER -