An impressive fact expressible in Presburger arithmetic?

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Is there anything expressible in Presburger arithmetic that would seem impressive to students at an undergraduate level?

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I don't know if this will impress anybody, but for fixed relatively prime $m$ and $n$ the fact that any number divisible by $m$ and $n$ is also divisible by $mn$ is expressible in Presburger arithmetic.

E.g., the assertion "$x$ is divisible by $5$" is expressed by the formula $$\exists y(x=y+y+y+y+y).$$