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111年 - 111 教育部公費留學考試試題：離散數學#125727
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5. [15%] Solve the recurrence equation given by:
a
n+2
- 2a
n
+ a
n+1
= 0, a
0
= 0, a
1
= 1.
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2. [10%] We flip a coin for 15 times and obtain a result of x times of coin facing up and y times of coin facing down. What is the most likely outcome of (x, y)? Apparently, we have x + y = 15. What is the probability to have such outcome (x, y)?
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3. [15%] Which series is bigger, ? We have:
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6. [15%] Which of the following graphs, K6 (complete graph with 6 vertices) or K7 (complete graph with 7 vertices) has closed Euler walk? Explain your answer as clear as possible. That is, in closed Euler walk, we allow each edge to be visited exactly once, and the initial vertex and ending vertex are the same. Can we modify the graph(s) to make it/them possible to contain a closed Euler walk?
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Def 1.A tree consists of a root, and zero or more subtrees T1, T2, ..., Tk. Also, there is an edge from the root to the rootof each subtree.
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Now someone modifies the definition and give the following alternative one:Def 2.A tree consists of a root, and one or more subtrees T1, T2,..., Tk. Also, there is an edge from the root to the root of each subtree.Can you describe what will happen if we choose the second one as the definition instead? What trees can be generated by the two definitions?
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2. 何謂主動式攻擊(Active Attack)?
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3. 被動式攻擊包含哪些攻擊方法(請具體描述每個攻擊方法及是針對 Confidentiality、Integrity、Availability 哪一項的攻擊)?
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