1. Let P(n) be the statement that a postage of n cents can be formed using...

 

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1. Let P(n) be the statement that a postage of n cents can be formed using just 4-cent stamps and 7-cent stamps. Conduct a strong induction proof to show that P(n) is true whenever n > 18. 2. Prove that V6 is irrational using strong induction. 3. Use strong induction to show that every positive integer n can be written as a sum of distinct powers of two, that is, as a sum of a subset of the integers 20 = 1, 2' = 2, 22 = 4, and so on. 4. Show that if a = b (mod m) and c= d (mod m), where a, b, c, d, and m are integers with m > 2, then a-c= b-d (mod m). 1. Let P(n) be the statement that a postage of n cents can be formed using just 4-cent stamps and 7-cent stamps. Conduct a strong induction proof to show that P(n) is true whenever n > 18. 2. Prove that V6 is irrational using strong induction. 3. Use strong induction to show that every positive integer n can be written as a sum of distinct powers of two, that is, as a sum of a subset of the integers 20 = 1, 2' = 2, 22 = 4, and so on. 4. Show that if a = b (mod m) and c= d (mod m), where a, b, c, d, and m are integers with m > 2, then a-c= b-d (mod m).