Please show all the steps and explain.
P(n): Every stamp of amount cents can be made using 4 and 7 cent stamps
Base case: 18 can be made as
Induction assumption: We can make stamps of using just 4 and 7 cent stamps
We will show that we can also made a stamp of cents
Note that can be made using 4 and 7 cent stamps means there exist non-negative a and b such that
So that is a valid way of making k+1 cent stamp
Unless in which case in which we can write
Which is a valid way of making k+1 stamps unless
Note that both and are not possible because then contradicting
So that we can always make a stamp of k+1 cents
So that by induction, we can always make a stamp of n cents when using 4-cent and 7-cent stamps
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Please show all the steps and explain. Prove that every amount of postage of 18 cents...
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