**Problem.** Are there natural numbers $a,b,c$ such that $ab$ divides $c^2-1$ and both equations

$$sum_{k=1}^bsum_{n=1}^a x_{k,n}e^{ipi n/a}=sqrt{c-1}$$

and

$$sum_{k=1}^bsum_{n=1}^a y_{k,n}e^{ipi n/a}=sqrt{c+1}$$

have solutions $x_{k,n}$, $y_{k,n}$ in the set ${-1,1}$?

**Remark.** This problem was motivated by some problem on decompositions of finite groups.