# FindInstance within a range

I am trying to find particular solutions to my inequality for two positive integers $a$ and $b$:

FindInstance[a<f[etc...]*b,{a,b},Integers]


However I want $a$ and $b$ to to be both above $10^3$. How may I achieve this? Is there a way to use Assumptions for this or some sort of magic along the lines of:

FindInstance[a<f[etc...]*b,{a,b},Integers,a>10^3 && b>10^3]


FindInstance[a < a*b && a > 10^3 && b > 10^3, {a, b}]