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For a set of integers $A$, the ratio set of $A$ is defined by $R(A):=\{a/b:a, b\in A, b\neq 0\}$. It is an open problem to study the denseness of $R(A)$in the $p$-adic numbers when $A$ is the set of nonzero values attained by anintegral form. In 2019, Donnay, Garcia and Rouse answered this problem forquadratic forms. Recently, we have studied this problem for the diagonal binarycubic forms $ax^3+by^3$, where $a$ and $b$ are integers. Later on, jointly withMiska, we extend the results on the diagonal binary cubic forms to the diagonalbinary forms $ax^n+by^n$ for all $n\geq 3$. In this article, we study thisproblem for the binary form $ax^d+bxy^{d-1}+cy^d$ of degree $d\geq 2$. Also, wegive a sufficient condition for the existence of infinitely many primes $p$such that the ratio set of the values assumed by an integral form is dense in$\mathbb{Q}_p$. Furthermore, we study the denseness of ratio sets of valuesassumed by cubic and quartic forms in two variables. A result for quintic formsis also discussed in the article.

On $p$-adic denseness of quotients of values of integral forms