Non-biodegradable

Number Theory Level 5

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.