$n$ such that the digits immediately after the decimal point of $pi^n$ give $n$ again

The name of the pictureThe name of the pictureThe name of the pictureClash Royale CLAN TAG#URR8PPP











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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.









share|cite|improve this question


















  • 1




    $n=0$ and $n=1$ work!
    – Blue
    Aug 20 at 11:21











  • Yes but I not getting higher values so that I can do work on making a general formula for this property
    – Adarsh Kumar
    Aug 20 at 11:23














up vote
-2
down vote

favorite
2












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.









share|cite|improve this question


















  • 1




    $n=0$ and $n=1$ work!
    – Blue
    Aug 20 at 11:21











  • Yes but I not getting higher values so that I can do work on making a general formula for this property
    – Adarsh Kumar
    Aug 20 at 11:23












up vote
-2
down vote

favorite
2









up vote
-2
down vote

favorite
2






2





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.









share|cite|improve this question














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.











share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Aug 20 at 11:20









Blue

43.8k868141




43.8k868141










asked Aug 20 at 11:06









Adarsh Kumar

519




519







  • 1




    $n=0$ and $n=1$ work!
    – Blue
    Aug 20 at 11:21











  • Yes but I not getting higher values so that I can do work on making a general formula for this property
    – Adarsh Kumar
    Aug 20 at 11:23












  • 1




    $n=0$ and $n=1$ work!
    – Blue
    Aug 20 at 11:21











  • Yes but I not getting higher values so that I can do work on making a general formula for this property
    – Adarsh Kumar
    Aug 20 at 11:23







1




1




$n=0$ and $n=1$ work!
– Blue
Aug 20 at 11:21





$n=0$ and $n=1$ work!
– Blue
Aug 20 at 11:21













Yes but I not getting higher values so that I can do work on making a general formula for this property
– Adarsh Kumar
Aug 20 at 11:23




Yes but I not getting higher values so that I can do work on making a general formula for this property
– Adarsh Kumar
Aug 20 at 11:23










1 Answer
1






active

oldest

votes

















up vote
2
down vote



accepted










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






share|cite|improve this answer






















  • Sir did you use any program to calculate these values?
    – Adarsh Kumar
    Aug 20 at 14:40






  • 1




    Yes, Mathematica.
    – Julián Aguirre
    Aug 20 at 14:40










  • Ok thanks a lot for giving your time for my question.
    – Adarsh Kumar
    Aug 20 at 14:41










  • 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.
    – Adarsh Kumar
    Aug 20 at 15:02










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1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes








up vote
2
down vote



accepted










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






share|cite|improve this answer






















  • Sir did you use any program to calculate these values?
    – Adarsh Kumar
    Aug 20 at 14:40






  • 1




    Yes, Mathematica.
    – Julián Aguirre
    Aug 20 at 14:40










  • Ok thanks a lot for giving your time for my question.
    – Adarsh Kumar
    Aug 20 at 14:41










  • 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.
    – Adarsh Kumar
    Aug 20 at 15:02














up vote
2
down vote



accepted










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






share|cite|improve this answer






















  • Sir did you use any program to calculate these values?
    – Adarsh Kumar
    Aug 20 at 14:40






  • 1




    Yes, Mathematica.
    – Julián Aguirre
    Aug 20 at 14:40










  • Ok thanks a lot for giving your time for my question.
    – Adarsh Kumar
    Aug 20 at 14:41










  • 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.
    – Adarsh Kumar
    Aug 20 at 15:02












up vote
2
down vote



accepted







up vote
2
down vote



accepted






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






share|cite|improve this answer














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







share|cite|improve this answer














share|cite|improve this answer



share|cite|improve this answer








edited Aug 20 at 14:45

























answered Aug 20 at 14:38









Julián Aguirre

65.2k23894




65.2k23894











  • Sir did you use any program to calculate these values?
    – Adarsh Kumar
    Aug 20 at 14:40






  • 1




    Yes, Mathematica.
    – Julián Aguirre
    Aug 20 at 14:40










  • Ok thanks a lot for giving your time for my question.
    – Adarsh Kumar
    Aug 20 at 14:41










  • 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.
    – Adarsh Kumar
    Aug 20 at 15:02
















  • Sir did you use any program to calculate these values?
    – Adarsh Kumar
    Aug 20 at 14:40






  • 1




    Yes, Mathematica.
    – Julián Aguirre
    Aug 20 at 14:40










  • Ok thanks a lot for giving your time for my question.
    – Adarsh Kumar
    Aug 20 at 14:41










  • 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.
    – Adarsh Kumar
    Aug 20 at 15:02















Sir did you use any program to calculate these values?
– Adarsh Kumar
Aug 20 at 14:40




Sir did you use any program to calculate these values?
– Adarsh Kumar
Aug 20 at 14:40




1




1




Yes, Mathematica.
– Julián Aguirre
Aug 20 at 14:40




Yes, Mathematica.
– Julián Aguirre
Aug 20 at 14:40












Ok thanks a lot for giving your time for my question.
– Adarsh Kumar
Aug 20 at 14:41




Ok thanks a lot for giving your time for my question.
– Adarsh Kumar
Aug 20 at 14:41












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.
– Adarsh Kumar
Aug 20 at 15:02




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.
– Adarsh Kumar
Aug 20 at 15:02












 

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