  Let A be a subset of Z / NZ, and let R be the set of large Fourier
coefficients of A. Properties of R have been studied in works of M.-C. Chang
and B. Green. Our result is the following : the number of quadruples (r_1, r_2,
r_3, r_4) \in R^4 such that r_1 + r_2 = r_3 + r_4 is at least |R|^{2+\epsilon},
\epsilon>0. This statement shows that the set R is highly structured. We also
discuss some of the generalizations and applications of our result.

Number Theory;Combinatorics