What is the smallest integer n such that $2^n equiv 3$ mod n? [closed]












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What is the smallest integer $nge2$ such that $2^n equiv 3 (mod n)$?






elementary-number-theory modular-arithmetic arithmetic







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closed as off-topic by 5xum, Adrian Keister, amWhy, Paul Frost, Michael Hoppe Dec 11 '18 at 15:22


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – 5xum, Adrian Keister, amWhy, Paul Frost, Michael Hoppe

If this question can be reworded to fit the rules in the help center, please edit the question.












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    Also, don't get discouraged by the downvote. I downvoted the question and voted to close it because at the moment, it is not up to site standards (you have shown no work you did on your own). If you edit your question so that you show what you tried and how far you got, I will not only remove the downvote, I will add an upvote.
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    Dec 11 '18 at 14:34
















1












$begingroup$


What is the smallest integer $nge2$ such that $2^n equiv 3 (mod n)$?






elementary-number-theory modular-arithmetic arithmetic







share|cite|improve this question











$endgroup$



closed as off-topic by 5xum, Adrian Keister, amWhy, Paul Frost, Michael Hoppe Dec 11 '18 at 15:22


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – 5xum, Adrian Keister, amWhy, Paul Frost, Michael Hoppe

If this question can be reworded to fit the rules in the help center, please edit the question.












  • 3




    $begingroup$
    Hi and welcome to the site! Since this is a site that encourages and helps with learning, it is best if you show your own ideas and efforts in solving the question. Can you edit your question to add your thoughts and ideas about it? Don't worry if it's wrong - that's what we're here for.
    $endgroup$
    – 5xum
    Dec 11 '18 at 14:34






  • 3




    $begingroup$
    Also, don't get discouraged by the downvote. I downvoted the question and voted to close it because at the moment, it is not up to site standards (you have shown no work you did on your own). If you edit your question so that you show what you tried and how far you got, I will not only remove the downvote, I will add an upvote.
    $endgroup$
    – 5xum
    Dec 11 '18 at 14:34














1












1








1


1



$begingroup$


What is the smallest integer $nge2$ such that $2^n equiv 3 (mod n)$?






elementary-number-theory modular-arithmetic arithmetic







share|cite|improve this question











$endgroup$




What is the smallest integer $nge2$ such that $2^n equiv 3 (mod n)$?






elementary-number-theory modular-arithmetic arithmetic




elementary-number-theory modular-arithmetic arithmetic






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Dec 11 '18 at 15:07







Bonbon

















asked Dec 11 '18 at 14:32









BonbonBonbon

32118




32118




closed as off-topic by 5xum, Adrian Keister, amWhy, Paul Frost, Michael Hoppe Dec 11 '18 at 15:22


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – 5xum, Adrian Keister, amWhy, Paul Frost, Michael Hoppe

If this question can be reworded to fit the rules in the help center, please edit the question.







closed as off-topic by 5xum, Adrian Keister, amWhy, Paul Frost, Michael Hoppe Dec 11 '18 at 15:22


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – 5xum, Adrian Keister, amWhy, Paul Frost, Michael Hoppe

If this question can be reworded to fit the rules in the help center, please edit the question.








  • 3




    $begingroup$
    Hi and welcome to the site! Since this is a site that encourages and helps with learning, it is best if you show your own ideas and efforts in solving the question. Can you edit your question to add your thoughts and ideas about it? Don't worry if it's wrong - that's what we're here for.
    $endgroup$
    – 5xum
    Dec 11 '18 at 14:34






  • 3




    $begingroup$
    Also, don't get discouraged by the downvote. I downvoted the question and voted to close it because at the moment, it is not up to site standards (you have shown no work you did on your own). If you edit your question so that you show what you tried and how far you got, I will not only remove the downvote, I will add an upvote.
    $endgroup$
    – 5xum
    Dec 11 '18 at 14:34














  • 3




    $begingroup$
    Hi and welcome to the site! Since this is a site that encourages and helps with learning, it is best if you show your own ideas and efforts in solving the question. Can you edit your question to add your thoughts and ideas about it? Don't worry if it's wrong - that's what we're here for.
    $endgroup$
    – 5xum
    Dec 11 '18 at 14:34






  • 3




    $begingroup$
    Also, don't get discouraged by the downvote. I downvoted the question and voted to close it because at the moment, it is not up to site standards (you have shown no work you did on your own). If you edit your question so that you show what you tried and how far you got, I will not only remove the downvote, I will add an upvote.
    $endgroup$
    – 5xum
    Dec 11 '18 at 14:34








3




3




$begingroup$
Hi and welcome to the site! Since this is a site that encourages and helps with learning, it is best if you show your own ideas and efforts in solving the question. Can you edit your question to add your thoughts and ideas about it? Don't worry if it's wrong - that's what we're here for.
$endgroup$
– 5xum
Dec 11 '18 at 14:34




$begingroup$
Hi and welcome to the site! Since this is a site that encourages and helps with learning, it is best if you show your own ideas and efforts in solving the question. Can you edit your question to add your thoughts and ideas about it? Don't worry if it's wrong - that's what we're here for.
$endgroup$
– 5xum
Dec 11 '18 at 14:34




3




3




$begingroup$
Also, don't get discouraged by the downvote. I downvoted the question and voted to close it because at the moment, it is not up to site standards (you have shown no work you did on your own). If you edit your question so that you show what you tried and how far you got, I will not only remove the downvote, I will add an upvote.
$endgroup$
– 5xum
Dec 11 '18 at 14:34




$begingroup$
Also, don't get discouraged by the downvote. I downvoted the question and voted to close it because at the moment, it is not up to site standards (you have shown no work you did on your own). If you edit your question so that you show what you tried and how far you got, I will not only remove the downvote, I will add an upvote.
$endgroup$
– 5xum
Dec 11 '18 at 14:34










1 Answer
1






active

oldest

votes


















3












$begingroup$

The smallest such integer is $4700063497$. See A036236.






share|cite|improve this answer









$endgroup$













  • $begingroup$
    Great! Thank you!
    $endgroup$
    – Bonbon
    Dec 11 '18 at 15:06


















1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes









3












$begingroup$

The smallest such integer is $4700063497$. See A036236.






share|cite|improve this answer









$endgroup$













  • $begingroup$
    Great! Thank you!
    $endgroup$
    – Bonbon
    Dec 11 '18 at 15:06
















3












$begingroup$

The smallest such integer is $4700063497$. See A036236.






share|cite|improve this answer









$endgroup$













  • $begingroup$
    Great! Thank you!
    $endgroup$
    – Bonbon
    Dec 11 '18 at 15:06














3












3








3





$begingroup$

The smallest such integer is $4700063497$. See A036236.






share|cite|improve this answer









$endgroup$



The smallest such integer is $4700063497$. See A036236.







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered Dec 11 '18 at 15:05









orlporlp

7,4341330




7,4341330












  • $begingroup$
    Great! Thank you!
    $endgroup$
    – Bonbon
    Dec 11 '18 at 15:06


















  • $begingroup$
    Great! Thank you!
    $endgroup$
    – Bonbon
    Dec 11 '18 at 15:06
















$begingroup$
Great! Thank you!
$endgroup$
– Bonbon
Dec 11 '18 at 15:06




$begingroup$
Great! Thank you!
$endgroup$
– Bonbon
Dec 11 '18 at 15:06



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