Answer to Question #149825 in Combinatorics | Number Theory for Wesam

Question

Compute the number of ordered triples of integers (a,b,c) between 1 and 12, inclusive, such that, if q =) a + ( 1 / b ) − ( 1 / (b + 1 / c )), then q is a positive rational number and, when q is written in lowest terms, the numerator is divisible by 13.

Answer 1

$q=\frac{ab(bc+1)+1}{b(bc+1)}$

I found 4 triples for a=1:

(1,1,11), q=13/12

(1,2,9), q=39/38

(1,4,7), q=117/116

(1,7,7), q=351/350