Random value from two seeds

Have a twodimensional grid and need a reproducible, random value for every integer coordinate on this grid. This value should be as unique as possible. In a grid of, let's say 1000 x 1000 it shouldn't occur twice.

To put it more mathematical: I'd need a function f(x, y) which gives an unique number no matter what x and y are as long as they are each in the range [0, 1000]

f(x, y) has to be reproducible and not have side-effects.

Probably there is some trivial solution but everything that comes to my mind, like multiplying x and y, adding some salt, etc. does not lead anywhere because the resulting number can easily occur multiple times. One working solution I got is to use a randomizer and simply compute ALL values in the grid, but that is too computationally heavy (to do every time a value is needed) or requires too much memory in my case (I want to avoid pre-computing all the values).

Any suggestions? Huge thanks in advance.