7
$\begingroup$

What made 142857 a special number? Why it gives the same digits if it is multiplied by 1,2,3,4,5 & 6 ? And gives all nines when it is multiplied by 7?

$\endgroup$
  • $\begingroup$ Please include source/motivation for this question. $\endgroup$ – tatan Aug 24 at 18:27
  • 1
    $\begingroup$ It just got struck in my head... And it started as a puzzle to me $\endgroup$ – user698179 Aug 24 at 18:30
  • $\begingroup$ It's $(10^6-1)/7$. $\endgroup$ – Lord Shark the Unknown Aug 24 at 19:06
9
$\begingroup$

More generally, this happens for the fraction $1/n$ exactly when $10$ is a primitive root mod $n$.

Those $n$ are the ones in A167797: $$ 7, 17, 19, 23, 29, 47, 49, 59, 61, 97, 109, 113, 131, 149, 167, 179, 181, 193, \dots $$

$\endgroup$
2
$\begingroup$

Because $\dfrac1{7} =.142857142857... $ and all (and there is a lot) that follows from that.

$\endgroup$
  • 1
    $\begingroup$ I don't think just mentioning this is helpful at all. The OP might have observed this besides you haven't mentioned how to further draw conclusions from this. $\endgroup$ – StackUpPhysics Aug 29 at 19:52
  • $\begingroup$ Thank you. Upvoted. $\endgroup$ – marty cohen Aug 29 at 23:11

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.