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

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
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