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轉學考-代數
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98年 - 98 淡江大學 轉學考 代數#55938
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題組內容
2. (15 points) Let
(a) Show that if a
2
+ b
2
is a prime in % iJicn a b√-l is a prime in R. Give an example f,o show I,hah the convcrae is not. trvio,
其他申論題
【已刪除】(2)以顯著水準0.05檢定北、中、南區的平均銷售量是否有差異。
#211893
【已刪除】1, (a) (10 poinlis) Let a，b Z and d - gcd{a, fc}. Show that there exists r s Z that ra+sb=d.
#211894
(b) (5 points) Let a，b and c bo, intege.vs. If a and c arc relatively prime, show that, c | ab itnplies that- c | b.
#211895
【已刪除】(c) (5 points) Show that, p Z is a prime if and only for all integers a and b, p | ah implies p | a or p 丨 b.
#211896
【已刪除】(b) such that
#211898
【已刪除】(c)
#211899
.3. (15 points) (a) Construct a field F over Q such l-hal; x7 +2x + 2 has a root, in F. Find the degree of extension of F over Q.
#211900
(h) Construct a finite field of 27 eloinctits.
#211901
(a) Show f,hat for any d | n, there is a subgroup of order d,
#211902
【已刪除】(b) Show filial; if (r, n) = d、tlion ad <ar>
#211903
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