Let your 4 digit number be aabb=x^2, where a and b are single digit numbers.
Then 11(100a+b)=x^2. Since 11 is a prime, 11 divides x, hence 11 divides (100a+b).
Consequently, 11 divides a+b (since 100a=99a+a). But 0
Therefore we have
9a+(a+b)/11=(x/11)^2,
or 9a+1=y^2, where we write y=x/11.
Finally since 9a=(y+1)*(y-1) and a can not be 11, so a=7 and b=11-a=4.
回複:四位平方數,前兩位和後兩位都相同,怎麽求?(知道是7744,但怎麽推呢?
所有跟帖:
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非常感謝!
-好吃客-
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06/13/2010 postreply
05:16:02
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A typo: "0<18" should be "0<a+b<=18"
-aisanguo-
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06/15/2010 postreply
17:30:34
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就隻是稍微囉嗦了那麽一點點
-7率-
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06/16/2010 postreply
10:33:03
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本末倒置。 LZ 直觀看出是7744,但希望知道如何理性推導出7744。
-皆兄弟也-
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06/16/2010 postreply
13:37:52
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既然你自己跳出來了,咱就拿你做個樣子娛樂大家吧
-7率-
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06/16/2010 postreply
15:28:38
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討論問題,請對網友用詞不要過激!
-皆兄弟也-
♂
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06/16/2010 postreply
20:12:31
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我用詞過激了嗎?那好!我道歉!對不起你的神經係統!
-7率-
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06/17/2010 postreply
02:10:15