What is the largest positive integer n for which there is a unique integer k such that
8/15 < n/(n+K) < 7/13
please help
$\displaystyle \frac{8}{15} < \frac{n}{n+K} < \frac{7}{13}$
Multiply by a common divisor of $\displaystyle 15$ and $\displaystyle 13$ so as to get everything in integers.
$\displaystyle \frac{104}{195} < \frac{195n}{195(n+K)} < \frac{105}{195}$
Multiply everything by $\displaystyle 195$ so we get integers ...
$\displaystyle 104 < \frac{195n}{n+K} < 105$
It might help ...
EDIT : oh, no ! owned by Pickslides ! (nearly the same contents though)