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102年 - 102 淡江大學 轉學考 代數#53069
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題組內容
1. (20 pts)
(b) What is the remainder when 35
35
is divided by 37?
其他申論題
4. Show the content of stack SI and the value of variables x and y after the following algorithm segments is executed. (10%) Stack(Sl); push(S 1, 5); push(Sl, 3); push(S 1, 2); If (not empty(Sl)) pop(Sl, x); If(not empty(S 1)) pop(Sl, y); Push(Sl,6)
#193072
5. Find the Huffman tree for the following characters using Huffman coding with the given frequencies: A(12), B(8), C(9), D(20), E(31), F(14), G(8). (15%)
#193073
6. Multiple Choice Questions (10%)
#193074
【已刪除】 (a) Suppose p is a prime number and a is an integer, (a,p) — 1. Prove that ap~11 (mod p).
#193075
2. (12 pts) Prove or disprove: If G is a group of order 53, then G must be cyclic.
#193077
3. (12 pts) Suppose G = {e, a, 6, c} is a group of order 4; but it contains no element of order 4. Write out the operation table for G.
#193078
(a) Prove that every finite integral domain is a field.
#193079
(b) Give an example of an integral domain which is not a field.
#193080
5. (12 pts) Show that the principal ideal (x — 1) in Z[x] is prime but not maximal. .
#193081
(a) Show that x3 + x + 1 is irreducible in Z5 [x].
#193082
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