I was doing something with value of $\pi$ as I know that the beauty of numbers will always exist , doesn't matter either number is real or complex it must be beautiful. I observe something strange by using Wolfram alpha's calculator:

$$ \pi^4 = 97.40909103400243723644033268870511124972758567268542169146... $$

as we can see the power of $\pi$ is $4$ and on right hand side the number after decimal place is also $4$.

Now a question arise in my mind:

"Is there any value also exist which can show the below relation as $4$ did?"

$$ \pi^n = ....ABCD.nPQRST....... $$ ( where n is the number after decimal which can be of any digits)

I still don't get any clue.Any hint or solution will helpful for me. Thanks.

  • 1
    $\begingroup$ $n=0$ and $n=1$ work! $\endgroup$ – Blue Aug 20 '18 at 11:21
  • $\begingroup$ Yes but I not getting higher values so that I can do work on making a general formula for this property $\endgroup$ – Dynamo Aug 20 '18 at 11:23

Next ones are $75$, $9\,424$ and $12\,669$. I do not see any pattern.

  • $\begingroup$ Sir did you use any program to calculate these values? $\endgroup$ – Dynamo Aug 20 '18 at 14:40
  • 1
    $\begingroup$ Yes, Mathematica. $\endgroup$ – Julián Aguirre Aug 20 '18 at 14:40
  • $\begingroup$ Ok thanks a lot for giving your time for my question. $\endgroup$ – Dynamo Aug 20 '18 at 14:41
  • $\begingroup$ Aguirre Sir if you have time can you solve my another related to Beal's conjecture, say yes only if you have time sir. because i don't want to waste your precious time. $\endgroup$ – Dynamo Aug 20 '18 at 15:02

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