Notation for an expression that is true for modular arguments

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I am trying to write clearly and compactly that a certain coefficient, with indices $k_1$ and $k_3$ is null unless both $k_1$ AND $k_3$ are integer multiples of the integer variable $s$. Right now I have:

$$t_{k_1}^{k_3} = 0 \ \ \forall \ \ k_1,k_3 \notin s\mathbb{Z}$$

Is this clear? Is there a more standard way of expressing this?