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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 …
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, …