(a) For c, d, n, m ∈ Z, with n > 1 and m > 0, prove that if c = d (mod n), then me = md (mod n) and cm = dm (mod n).
b) If xnxn-1 ∙∙∙∙∙∙∙ x1\x0 = xn • 10 + ∙∙∙∙∙∙ + x\ • 10 + x0 denotes an (n + 1)-digit integer, then prove that
xnxn-i ∙∙∙∙∙∙∙∙ x1x0 = xn + xn-1 +∙∙∙∙∙∙∙∙∙+ x1 + x0 (mod 9).