On squares in polynomial products

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


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 languageEnglish
Pages (from-to)215-223
Number of pages9
JournalMonatshefte fur Mathematik
Issue number3
Publication statusPublished - Jan 2010


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