Note on a Reconstruction Problem for Number Sequences

摘要

The authors consider the following problem: for which values of n can the211u001esequence a(sub 1),...,a(sub n) of real numbers be reconstructed (up to order) 211u001efrom the sequence S(sub 1),...,S(sub m) of the sums a(sub i) + a(sub j) (1 < or + 211u001ei < j < or + n, m = ((sup n)(sub 2))). The answer is positive for n = 3, 5, 6, 211u001eand its negative for n = 2(sup k) (k > or = 0).