a^k-b^k=a-bM

a^k+1-b^k+1

=a(a^k)-b(b^k)

=a[(a-b)M+b^k]-b(b^k)

=a-b (aM) + a(b^k)-b(b^k)

=a-b(aM) + (a-b) (b^k)

=(a-b)(aM+b^k)

p(k+1) 成立