- 1.
Use Euclidean Algorithm to find the great common divisor of 7n + 3 and 5n + 2 (n ∈ N).
- 題型：問答題
- 難易度：尚未記錄
- 2.
Prove that if we select 101 integers from the set S = {1, 2, 3, …, 200}, there exist two integers m, n in the selection where gcd(m, n) = 1.
- 題型：問答題
- 難易度：尚未記錄
- 3.
With A = {x, y, z}, let f, g : A → A be given by f = {(x, y), (y, z), (z, x)}, g = {(x, y), (y, x), (z, z)}. Determine each of the following: f o g, g−1, (g o f)−1, f−1 o g−1, and g−1 o f−1.
- 題型：問答題
- 難易度：尚未記錄
- 4.
For the finite state machine given in the following table, determine a minimal machine that is equivalent to it.
- 題型：問答題
- 難易度：尚未記錄
- 5.
Let the input alphabet I and out alphabet O be both {0, 1}. Construct a state diagram for a finite state machine that reverses (from 0 to 1 or from 1 to 0) the symbols appearing in the 4th, in the 8th, in the 12th, …, position of an input string x ∈ I+. For example, if s0 is the starting state, then ω(s0, 0000) = 0001, ω(s0, 000111) = 000011, and ω(s0, 000000111) = 000100101. (Here ω is the output function.)
- 題型：問答題
- 難易度：尚未記錄
- 6.
Let A be a set with |A| = n and R be a relation on A that is antisymmetric. How many R can be defined?
- 題型：問答題
- 難易度：尚未記錄
- 7.
How many ways can we select seven nonconsecutive integers from {1, 2, 3, 4, …, 50}?
- 題型：問答題
- 難易度：尚未記錄
- 8.
Find the chromatic polynomials of the following graph.
- 題型：問答題
- 難易度：尚未記錄