Non-biodegradable

Find the largest possible integer value of NN such that gcd(N,2033)=1 \gcd(N, 2033) = 1 and N2033 \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 1702033=1214+338 \frac{ 170} { 2033} = \frac{1}{214} + \frac{ 3 }{38 } , hence the answer is not 170.

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