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102年 - 102 國立中山大學_碩士班招生考試_電機系(丙組)：離散數學#108985
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題組內容
2.Given a number x = 3293 13600, please answer the following questions.
(a) How many positive divisors does x have? [5%]
其他申論題
(a) Fundamental Theorem of Arithmetic
#467062
(b) Homeomorphic graph
#467063
(c) Equivalence relation
#467064
(d) Four-color Theorem
#467065
(6) How many positive divisors of x that are divisible by 252? [5%]
#467067
(c) Determine how many positive divisors of x are perfect squares? [5%]
#467068
(a) If an equivalence relation R on set A = {1,2,3,4,5}induces the partition A = {1,3} ∪{2,4} ∪{5}, what is R? [5%]
#467069
(b) Let R={(1,1),(1,2),(2,2),(2,4), (3,3),(3,4),(4,5),(5,5)}be a relation on A. What is the relation R3 ? [5%]
#467070
4.What is the Ferrers graph? Use it to explain the statement "The number of partitions of an integer n into m summands is equal to the number of partitions of n into summands where m is the largest summand". [10%]
#467071
5. Use the generating function to find the number of integer solutions of the equationx1 +x2 +x3 +x4 =20, where -3 ≤ x1,-3 ≤ x2,-5 ≤ x3 ≤5, and 0≤x4.[15%]
#467072
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