# Unsimplifying a Fraction

**Number Theory**Level 4

Find the smallest positive integer \(N \neq 23\) such that the fraction \( \frac {N-23} { 7N+6 } \) is not in simplest terms.

**Details and assumptions**

A fraction \(\frac{a}{b}\) is **in simplest terms** if \(a\) and \(b\) are coprime integers.

As a specific example, the fraction \( \frac {6}{4} \) is not in simplest terms since \( \gcd(4, 6) = 2 \neq 1\). It can be simplified to \( \frac {3}{2} \).