Unformatted text preview: n is a natural number, and n ≥ 11. To save time, you may use the fact that: n 3 = ( n1) 3 + 3 n 23 n + 1 . 5. (2 points) Let F n be the Fibonacci sequence, given recursively by the following: • F = 1, and F 1 = 1. • If n ∈ N , and n ≥ 2, then F n = F n1 + F n2 . Prove that if n ∈ N , and if F n is even, then F n +1 is odd. 6. (3 points) Let S be the set of ordered triples ( x,y,z ), such that x,y,z ∈ Z , x > 0, y > 0, z > 0, and x + y + z = 100. For example, (1 , 9 , 90) ∈ S , and (40 , 40 , 20) ∈ S . How many elements does S have?...
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 Fall '08
 Weissman
 Math, Set Theory, Natural number, FN, Martin H. Weissman

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