If one computes 1/n where n is a positive integer sometimes one
obtains a pattern of digits where there is no initial string of
digits but only a repeating pattern. (For example: 1/3 or 1/7).
If the period of the repeating pattern is n-1 one can show that
n must be prime. (For example, 17 and 19.) However, there are
many primes p for which the repeat period is less than p-1. (For
example 11 or 13.)
1. For each integer i is there a prime which has repeat period
2. Is there any relation between the digits in the repeated pattern
and the prime or the digits in the prime?
3. Is there a pattern in the values of the primes for which the
repeats have the same length k?
1. Examine questions such as the above where the number is expressed
in a base other than 10.
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