# 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 $$\frac {3}{2}$$.

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