Let m, n > z be positive integers and let a_1, a_2, ..., a_n be positive integers which are not multiples of m^n-1.
Show that there exist integers c_1, c_2, ... c_n and d_1, d_2, ... d_n where |c_i| < m and |d_i| < m for all i = 1, 2, ..., n and (c_1, c_2, ... c_n) + (d_1, d_2, ... d_n) and sum(i=1,n(c_i*a_i)) = sum(i=1,n(d_i*a_i))mod m^n.