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

Who cares? and why?

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