All right, in the same vein as this thread. Suppose that p/q does not have a terminating representation in base n. I seem to recall reading that the repeating portion of p/q must have fewer than q digits. Is this true? If so, how would I prove it? I tried using the old algorithm for converting repeating decimals into fractions, but I couldn’t get anywhere with that.
Think about performing long division to produce the decimal. There’s only q - 1 possible non-zero remainders. As soon as you repeat a remainder, you repeat the pattern from the last point you obtained that remainder.
:smack: