# A Bunch of Irreducible Fractions

Number Theory Level 5

Find the smallest positive integer value of $$n$$ for which all of the fractions $$\dfrac{7}{n+9}$$, $$\dfrac{8}{n+10}$$, $$\dfrac{9}{n+11}$$, $$\dfrac{10}{n+12}$$, $$\ldots$$, $$\dfrac{2014}{n+2016}$$ are in lowest terms.

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