It is shown that if \(p\) is prime and \(\mathcal A, \mathcal B, \mathcal C, \mathcal D\) are large subsets of \(\mathbb Z_p\), then the equation \(ab+1=cd, a\in \mathcal A, b\in \mathcal B, c\in \mathcal C, d\in \mathcal D\) has a solution. This is a multiplicative analogue of the author’s earlier result where it was shown that the equation \(a+b=cd\) has a solution. Several interesting known and new results are shown to follow as a consequence, such as the solvability of both Legendre symbol equations \((\frac{a+b}{p})=1\) and \((\frac{a'+b'}{p})=-1\), where \(a'\in \mathcal A, b'\in \mathcal B\). The proof uses simple combinatorial arguments and summation techniques.