Suppose that a store offers gift certificates in denominations of25 dollars and 40 dollars. Determine the possible total amounts you can form using these gift certificates.
Prove your answer using strong induction.
It's an old problem, and the answer is that any amount above $140, which is divisible by 5 is available in gift certificates in 25 and 40 dollars.
The basis for the induction can start from $140, but let's determine all possible values of the expression 25x+40y below 160:
Strong induction is integrated.