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8. (a) How many vertices and how many edges are there in the complete bipartite graphs , where m,n ∈ Z⁺.

其他申論題

5. In how many ways can 3600 identical envelopes be divided, in package of 25, among five student groups so that each group get at least 150, but not more than 1000, of the envelopes?

(a) each summand must appear an even number of times；

(b) each summand must be even.

7. If ,n ≥ 0, is the unique solution of the recurrence relation = 0, and a2 = 156/77, = 1628/6336, what is d?

(b) If the graph has 72 edges, what is m?

9. For a, b,n ∈ Z⁺ and n ＞ 1, prove that a ≡ b (mod n) gcd(a,n) = gcd(b,n).

1.All circulant matrices are made diagonal by the Discrete Fourier Transform (DFT), regardless of the generating vector x.

2..DFT matrix is not a kind of symmetric matrix.

3. DFT matrix is an unitary matrix.

4.The DFT is a linear transform.

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