simplifying expressions - How to make Mathematica simplify $cos[(i + j + k)pi]$ to $(-1)^{i+j+k}$?

We know that: $$ \cos\left[(i+j+k)\pi\right] = (-1)^{i+j+k} $$ for $i, j, k$ being positive integers. In Mathematica I've tried:

FullSimplify[Cos[(i + j + k)*Pi], Assumptions -> Element[{i, j, k}, {Positive, Integers}]]

But it still returns the Cos function. Does anyone know how to perform this simplification?

Answer

Here's another way:

 Assuming[Element[{i, j, k}, Integers], Refine[Cos[(i + j + k) Pi]]]

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Comments

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