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. analytic geometrycombinatorics proposedcombinatorics