1. The problem statement, all variables and given/known data Hi everybody, I am trying to find the solution to this system of equations for a bigger physics problem: h+k+l=2n+1 with n=0,1,2,3... ei(π/2)(h+k+l)+ei(π/2)(3h+3k+l)+ei(π/2)(3h+k+3l)+ei(π/2)(h+3k+3l)=0 2. Relevant equations None 3. The attempt at a solution Ihave tried to solve it by taking the common factor ei(π/2) out and trying to solve e(h+k+l)+e(3h+3k+l)+e(3h+k+3l)+e(h+3k+3l)=0 by using h+k+l=0; then, I arrive to 1+e2k+2h+e2h+2l+e2k+2l=0. From here I don't know how to keep going, so if anybody could point me what to do next it wolud be very helpfull. Thanks for reading.