Show that if n is a product of m distinct primes, then the period of the decimal expansion of 1/n is the lowest common multiple of the periods of 1/p over all primes p|n. I understand that the above ...
Am I right to assume that: all rational numbers have a recurrent sequence in their decimal expansion, and the length of the expansion of $1/p$, where $p$ is prime, is $p-1$ for sufficiently large ...
I.e., is there a sequence of primes whose decimal expansions have the following form: $$a_1,\ a_1a_2,\ a_1a_2a_3,\ a_1a_2a_3a_4, \dots$$ What about with the order of the digits reversed, so each ...
Show that a number has a terminating decimal expansion if and only if, it is rational and when in lowest terms, its denominator is coprime to all primes other than $2$ and $5$. This is an unsolved ...
The number $142,857$ is widely known as a cyclic number, meaning consecutive multiples are cyclic permutations, i.e. $1 × 142,857 = 142,857$ $2 × 142,857 = 285,714$ $3 × 142,857 = ...
I have been thinking a little bit about the binary decimal expansion of reciprocal prime numbers; and I have a few questions. I found this neat table which lists the binary expansion of many ...