 Erdős–Graham problem

In combinatorial number theory, the Erdős–Graham problem is the problem of proving that, if the set {2, 3, 4, ...} of integers greater than one is partitioned into finitely many subsets, then one of the subsets can be used to form an Egyptian fraction representation of unity.That is, for every "r" > 0, and every "r"-coloring of the integers greater than one, there is a finite monochromatic subset "S" of these integers such that

In more detail, Paul Erdős and Ronald Graham conjectured that, for sufficiently large "r", the largest member of "S" could be bounded by "br" for some constant "b" independent of "r".