259. Coprime numbers. In which number systems are the numbers 35 and 58 coprime?
259. Let the greatest common divisor of numbers $x$ and $y$ be denoted by $(x, y)$. Then

$$
(35,58)=(35,23)=(12,23)=(12,11)=(1,11)=1
$$

Therefore, 35 and 58 are coprime in any number system with a base $>8$.

[D. Silverman, M. M., 38, 326 (November 1965).]