14.5.6 * 8 cents and 15 cents stamps can be used without limit. Some postage amounts, such as 7 cents, 29 cents, cannot be made up exactly. Find the largest amount $n$ that cannot be made up, and prove your conclusion.
Analysis: Since $98=8 \cdot 1+15 \cdot 6, 99=8 \cdot 3+15 \cdot 5, 100=8 \cdot 5+15 \cdot 4, 101=$ $8 \cdot 7+15 \cdot 3, 102=8 \cdot 9+15 \cdot 2, 103=8 \cdot 11+15 \cdot 1, 104=8 \cdot 13, 105=15 \cdot 7$, numbers greater than 105 can be obtained by adding appropriate multiples of 8 to the above expressions. However, 97 cannot be expressed using 8 and 15, so the required $n-97$.

Comment: We have the conclusion: When positive integers $a, b$ are coprime, the largest integer that cannot be expressed using $a, b$ is $a b-a-b$.