un 2 00 9 Base - 3 Repunit Primes and the Cantor Set
نویسنده
چکیده
The middle-third Cantor set C3 is a fractal consisting of all the points in [0, 1] which have non-terminating base-3 representations involving only the digits 0 and 2. I prove that all prime numbers p > 3 whose reciprocals belong to C3 must be base-3 repunit primes, and, conversely, that the reciprocals of all base-3 repunit primes must be in C3. This one-one correspondence appears to be unique to the base-3 case. 2000 Mathematics Subject Classification: Primary 11A41.
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تاریخ انتشار 2009