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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