Hello all, if $a_1,a_2, \ldots a_t$ are $t$ integers $\geq 2$, the set $G(a_1,a_2, \ldots a_t)=\lbrace N \geq 1 |$ In any sequence of $N$ consecutive integers there is at least one …

Hello all, Dirichlet's famous theorem asserts that any arithmetic progression $\lbrace ax+b | x \in {\mathbb N}\rbrace$ contains infinitely many primes if a and b are relatively pr …

This question is not homework, just asked out of curiosity. I wondered how many zeroes could be found at the end of $1990!$ . I computed something that seemed to work and found out …

(This is a follow-up question from over there: Natural models of graphs.) (And it has a follow-up question over there: Naturally definable sets of natural numbers (2): Can the cir …

On Wikipedia, there is a list of properties of sets of reals, which are in some sense "interesting": just have a look. I could not find a comparable list of properties of sets of …

Are there examples of sets of natural numbers that are proven to be decidable but by non-constructive proofs only?

[This shall be the last of a series of questions, see Naturally definable sets of natural numbers (2)] I cannot explain why I have been so stubborn not to see the most straight-fo …

The classic puzzle goes something like this: "You are standing in front of a lake with a 3 gallon bucket and a 5 gallon bucket, how can you get 4 gallons of water?" Is there an ea …

9 = 2^X mod 11 What is X and how do you find X?