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After publishing his recent paper in SIAM J. Appl. Math, 74, 392-410, 2014the author has realized that actually he has addressed in that paper, for thefirst time, a long standing open question being unaware about this. Thisquestion is about the uniqueness of a 3-d inverse scattering problem withoutthe phase information. Thus, it makes sense in the current paper to explicitlymake the latter statement and to formulate corresponding uniqueness theorems.

On the first solution of a long standing problem: uniqueness of the phaseless quantum inverse scattering problem in 3-d