Fractions 1/m and 1/n

enzocreti · 2020-03-04, 10:51

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

Uncwilly · 2020-03-05, 06:33

Who cares? and why?

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

2020-03-04, 10:51	#1
enzocreti Mar 2018 7²·11 Posts	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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2020-03-05, 06:33	#2
Uncwilly 6809 > 6502 """"""""""""""""""" Aug 2003 101×103 Posts 2B11₁₆ Posts	Who cares? and why? With such a limited set you should be able to write code and brute force an answer.