Why $142857$ when multiplied by $1$ to $6$ gives the same digits?

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: $$ 7, 17, 19, 23, 29, 47, 49, 59, 61, 97, 109, 113, 131, 149, 167, 179, 181, 193, \dots $$


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

Tags:

Arithmetic

Recreational Mathematics

Algebra Precalculus

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