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8 points

It’s definitely not an integer seeing as it has a fractional component. Do you mean if it’s rational or not?

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4 points
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No, we can’t proof if its an integer or not. If you can proof it, you are up for a great career in mathematics: https://www.spektrum.de/kolumne/ist-pi-hoch-pi-hoch-pi-hoch-pi-eine-ganze-zahl/2203268

(Unfortunately only found this german article, but maybe translation works)

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