programming an equation

Hello. I have read your paper and, actually, it seems like I know the solution and it is very simple one. if a = a₁ + a₂ + a₃ mod m, you can assume a₁ and a₂ absolutely random values in Zm, and a₃ = a - a₁ - a₂ mod m (more precisely — a₃ = 2m + a - a₁ - a₂ mod m). That is all, I assume.