4. (a) Show that if n is any integer, then precisely one of n – 1, n, and n +1 is divisible by 3. Hint. Use the division algorithm.

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4. (a) Show that if n is any integer, then precisely one of n – 1, n, and n +1 is divisible
|
by 3.
Hint. Use the division algorithm.
(b) For eachn e N, show that Fn is even if and only if 3 | n, where Fn is the nth
Fibonacci number.
Hint. In your inductive step to prove the result for n+1, break it into two cases:
n +1 is divisible by 3 and n+1 is not divisible by 3.
Transcribed Image Text:4. (a) Show that if n is any integer, then precisely one of n – 1, n, and n +1 is divisible | by 3. Hint. Use the division algorithm. (b) For eachn e N, show that Fn is even if and only if 3 | n, where Fn is the nth Fibonacci number. Hint. In your inductive step to prove the result for n+1, break it into two cases: n +1 is divisible by 3 and n+1 is not divisible by 3.
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