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Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions

10 votes

Undecidable easy arithmetical statement

To talk about undecidability, you have to specify the system. I consider the simplest system in which you can do real mathematics a system with proof strength $I\Sigma_1$ (feel free to disagree). In …
Lucas K.'s user avatar
  • 1,659
2 votes

Can we color Z^+ with n colors such that a, 2a, ..., na all have different colors for all a?

I suggested in a comment, to look for colorings that are the same for each a, except for a fixed permutation. Suppose the colors are given by function c(x), for x ≥ 1. And a permutation function p(i, …
Lucas K.'s user avatar
  • 1,659