Non-biodegradable

Find the largest possible integer value of \(N\) such that \( \gcd(N, 2033) = 1 \) and \( \frac{N}{2033} \) cannot be written as the sum of two positive rational numbers, each with denominators strictly less than 2033.

Details and assumptions

As an explicit example, since \( \frac{ 170} { 2033} = \frac{1}{214} + \frac{ 3 }{38 } \), hence the answer is not 170.

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