set of positive integers of the form 19a+85b
Source: bmo 1985
April 23, 2007
analytic geometrycombinatorics proposedcombinatorics
Problem Statement
Let be the set of all positive integers of the form , where are arbitrary positive integers. On the real axis, the points of are colored in red and the remaining integer numbers are colored in green. Find, with proof, whether or not there exists a point on the real axis such that any two points with integer coordinates which are symmetrical with respect to have necessarily distinct colors.