Abstract
For A⊆{1,2,…}, we consider R(A)={a/a′:a,a′∈A}. If A is the set of nonzero values assumed by a quadratic form, when is R(A) dense in the p-adic numbers? We show that for a binary quadratic form Q, R(A) is dense in Qp if and only if the discriminant of Q is a nonzero square in Qp, and for a quadratic form in at least three variables, R(A) is always dense in Qp. This answers a question posed by several authors in 2017.
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