I am instructed to prove that postage amounts greater than or equal to 54 can be taken care of using solely 7 and 10 cent stamps. The book asks me to use strong induction.
My Basis is:
54 = 4*10 + 2*7
My inductive step is:
(assume n = 10*j + 7*k for some n >= 54 and j,k are integers)
n + 1 = 10(j - 2) + 7(k + 3)
So the inductive step infers (as far as I can see) that if the hypothesis is true for n, it is true for n + 1. The basis is shown to be true.
It seems to me that this concludes a proof by WEAK induction, but the solutions manual presents a nearly identical argument and calls it strong induction.