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A puzzle related to mathematical facts and objects, whose solution needs mathematical arguments. General mathematics questions are off-topic but can be asked on Mathematics Stack Exchange.

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Four π's to make any integer

I also thought of Dirac's formula. Here's a formula for an arbitrary fraction: $$\pm {m \over n} = \pm { \ln { \ln \sqrt { \sqrt { \cdots \sqrt {\pi}}} \over \ln \pi } \over \ln { \ln \sqrt { …
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