... e, this yields e + 2ef = 0, and similarly f + 2ef = 0,so that f = −2ef = e, hence e = f = g by symmetry. Hence, finaly, 3e = e + f + g = 0,i.e. e = f = g = 0.For part (i) just omit some of this.Problem ... into n smaller cubes may be refined togive a dissection into n + (ad− 1) cubes, for any a ≥ 1. This refinement is achieved bypicking an arbitrary cube in the dissection, and cutting it into adsmaller ... =c∈S1µ(p − 1, c) = n. (1)The polynomial phas at most n − 1 roots (n > 0 is used here). This implies thatc∈S0∪S1µ(p, c) ≤ n − 1. (2)If p(c) = 0 or p(c) − 1 = 0, thenµ(p, c)...