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In our Reptand prime family, as you know, everybody has our own signature Cycle length. My younger sibling unit has shorter cyclic period and he wanted to create little puzzle for you.

He truncated his cyclelength to five digits. He says if you place 1 at the end of truncated unit, it becomes 3 times larger than if you placed at the beginning of the unit.

What are his signature cycle digits?. He says you don’t have to know him at all to do it.

Show how you deduced it without knowing him?

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  • $\begingroup$ A repunit is usually a number consisting only of ones (units), e.g. 111 or 11111. Does the meaning of this word in the puzzle differ from the usual one? $\endgroup$ – trolley813 May 16 at 7:30
  • $\begingroup$ Reptand primes have their own unique cyclic signature that repeats..it is called repunit. It’s length depends on the number. $\endgroup$ – Uvc May 16 at 7:42
  • $\begingroup$ It's usually called a repetend (or a reptend, depends on spelling). $\endgroup$ – trolley813 May 16 at 7:47
  • $\begingroup$ I will edit it to avoid confusion $\endgroup$ – Uvc May 16 at 8:12
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Not sure if this is the end...

Let the 5-digit number be $R$.
$10R + 1 = 3(100000 + R)$
$10R + 1 = 300000 + 3R$
$7R = 299999$
$R = 42857$

So, apparently,

You mean $1/7=0.142857182857...?$

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  • $\begingroup$ Given it is truncated, you need at least another digit,,.yes $\endgroup$ – Uvc May 16 at 11:25

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