-1
votes
1answer
725 views

Implication for m-cycles in Collatz-type problems.

Background Consider Collatz-type problems of the form $an + 1$, where $a > 2$ is a positive, odd integer (e.g., $3n + 1$, $5n +1 $, $7n + 1$, etc.). For convenience, automatically divide by two. ...
3
votes
2answers
363 views

Drawing (graphs) by numbers: a minimality question

Every simple graph $G$ can be represented ("drawn") by numbers in the following way: Assign to each vertex $v_i$ a number $n_i$ such that all $n_i$, $n_j$ are coprime whenever $i\neq j$. Let $V$ be ...
23
votes
3answers
3k views

Bringing Number and Graph Theory Together: A Conjecture on Prime Numbers

Some MOers have been skeptic whether something like natural number graphs can be defined coherently such that every finite graph is isomorphic to such a graph. (See my previous questions [1], [2], ...
4
votes
4answers
745 views

Prime numbers p not of the form ab + bc + ac (0 < a < b < c ) (and related questions)

If we ask which natural numbers n are not expressible as n = ab + bc + cd (0 < a < b < c) then this is a well known open problem. Numbers not expressible in such form are called Euler's ...