Proofs of Existence and Optimality · Difficult Problems in Number Theory (Optional)

Lesson 1

Nikolai Chukhin · Alexander S. Kulikov

This section explores number theory questions that begin with “Does there exist a number…?”—some of the simplest to state, yet notoriously difficult to solve (and in some cases still open).

Treat these as curiosities rather than core material: each problem is worth just one point, so don't spend too much time on them. Feel free to skip this lesson entirely—nothing here will be needed later.