6 You are given that \(n\) is an integer.
- (a) Show that \(\operatorname { hcf } ( 2 n + 1,3 n + 2 ) = 1\).
(b) Hence prove that, if \(( 2 n + 1 )\) divides \(\left( 36 n ^ { 2 } + 3 n - 14 \right)\), then \(( 2 n + 1 )\) divides \(( 12 n - 7 )\). - Use the results of part (i) to find all integers \(n\) for which \(\frac { 36 n ^ { 2 } + 3 n - 14 } { 2 n + 1 }\) is also an integer.