Geodesic
The Cardinalities of A+A and A-A
Canadian mathematical bulletin, Tome 16 (1973) no. 3, pp. 343-345

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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. 
Stein, Sherman K. The Cardinalities of A+A and A-A. Canadian mathematical bulletin, Tome 16 (1973) no. 3, pp. 343-345. doi: 10.4153/CMB-1973-055-6
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     title = {The {Cardinalities} of {A+A} and {A-A}},
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