1. Use strong mathematical induction to show that any postage of at least 18¢ can be obtained using 4¢ and 7¢ stamps.

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Fibonacci's Rabbits Leonardo Fibonacci da Pisa (c. 1170-1250), an outstanding European mathematician of the middle ages stated an interesting problem in his main work Liber Abaci (1202) where he wanted to know how many pairs of rabbits will be produced in a year, beginning with a single pair, if in every month each pair brings forth a new pair that becomes productive from the second month on and assuming no pairs die. Therefore, starting with F1 = 1 newly born pair in the first month, we can find the number Fk of pairs in the kth month. Using some knowledge of calculus, acquired when studying sequences, we can determine the number of pairs of rabbits in the kth month by setting up the following equation: Fk = (Number of pairs alive the preceding month) + (Number of newly born pairs for the kth month) Since the rabbits do not produce offsprings during the first month of their lives, we can see that the number of newly born pairs for the kth month is the number Fk - 2 of pairs alive…

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