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.

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 5 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.