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If we have a function $f$ with the property:

$$f: \mathbb{Z} \rightarrow \mathbb{Z}$$

and if we have a congruence over $\mathbb{Z}$ like so:

$$y\equiv z\pmod{n}$$

What are the conditions to then applying the arbitrary function to both sides?

$$f(y)\equiv f(z)\pmod{n}$$

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    What is $x$ in the equality? Do you mean for all $x$, or only for certain $x$? – 2017-02-15
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    I suppose $x$ would be an integer, should i write that in the question? – 2017-02-15
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    Something like $f: \mathbb{Z} \rightarrow \mathbb{Z}$ is definitely missing. Also $f$ invertible – 2017-02-15

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