1. ## Arithmetic problem

What is the largest positive integer n for which there is a unique integer k such that

8/15 < n/(n+K) < 7/13

$\frac{8}{15} < \frac{n}{n+K} < \frac{7}{13}$

$\frac{104}{195} < \frac{n}{n+K} < \frac{105}{195}$

$104 < \frac{195n}{n+K} < 105$

3. $\frac{8}{15} < \frac{n}{n+K} < \frac{7}{13}$

Multiply by a common divisor of $15$ and $13$ so as to get everything in integers.

$\frac{104}{195} < \frac{195n}{195(n+K)} < \frac{105}{195}$

Multiply everything by $195$ so we get integers ...

$104 < \frac{195n}{n+K} < 105$

It might help ...

EDIT : oh, no ! owned by Pickslides ! (nearly the same contents though)