Bijection from natural numbers to integer lattice
Source: Serbian National Olympiad 2012, Problem 5
April 4, 2012
combinatorics proposedcombinatorics
Problem Statement
Let be two-dimensional integer lattice. Is there a bijection , such that for every distinct we have: \gcd(a,b,c)>1 \Rightarrow f(a),f(b),f(c) \mbox{ are not colinear? }