BALKAN 1985 Problem 3

Let $S$ be the set of all positive integers of the form $19a+85b$ , where $a,b$ are arbitrary positive integers. On the real axis, the points of $S$ are colored in red and the remaining integer numbers are colored in green. Find, with proof, whether or not there exists a point $A$ on the real axis such that any two points with integer coordinates which are symmetrical with respect to $A$ have necessarily distinct colors.