# Reducto reducto reducto

Number Theory Level pending

Find the smallest positive integer $$N$$, such that the fractions

$\frac{1}{N+21}, \frac{2} {N+22}, \ldots, \frac{301} { N + 321}$

are all in lowest terms.

Details and assumptions

The fraction $$\frac{a}{b}$$ is in lowest terms if $$a$$ and $$b$$ are coprime.

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