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Old 2020-03-04, 10:51   #1
enzocreti
 
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Default Fractions 1/m and 1/n

Let be m,n two distinct integers with m,n<=559




Are there two fractions 1/m and 1/n such that the great common divisor of their recurring decimal digits is greater than 23255813953488372093?




1/344 and 1/559 is the record I found




infact the great common divisor of 9069...627 and 1788...100 is 23255813953488372093.


9069... is the periodic decimal expansion of 1/344
1788...100 is the periodic decimal expansion of 1/559
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Old 2020-03-05, 06:33   #2
Uncwilly
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Who cares? and why?

With such a limited set you should be able to write code and brute force an answer.
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