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
AN - SCOPUS:75549091060
SN - 0026-9255
VL - 159
SP - 215
EP - 223
JO - Monatshefte fur Mathematik
JF - Monatshefte fur Mathematik
IS - 3
ER -