Monochromatic Schur triples in randomly perturbed dense sets of integers

Given a dense subset A of the first n positive integers, we provide a short proof showing that for p = ω(n^-2/3), the so-called randomly perturbed set A∩ [n]_p a.a.s. has the property that any 2-coloring of it has a monochromatic Schur triple, i.e., a triple of the form (a, b, a + b). This result is optimal since there are dense sets A, for which A ∩ [n]_p does not possess this property for p = o(n^-2/3).