H. T. Croft's Research Problems, 1967, contains the following problem due to J. H. Conway. "Let A = {a1, a2,…, aN
} be a finite set of integers, and define
and
Prove that A—A always has more members than A+A, unless A is symmetric about 0."Marica in [1] showed that the conjecture is false for the set A = {1, 2, 3, 5, 8, 9, 13, 15, 16}. In this case A+A has 30 elements and A—A has 29 elements.