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The opinions expressed herein are my own personal opinions and do not represent anyone else's view in any way, including those of my employer.
© Copyright 2013
The opinions expressed herein are my own personal opinions and do not represent anyone else's view in any way, including those of my employer.
© Copyright 2013
進階教學(9)—-xyz=720的整數解問題
方程式 xyz=720
(1)有幾組正整數解
(2)整幾組整數解
(詳解)
(1)
先把720寫成標準分解式720=24 x3 2 x5
這意思是有
4個 2(想成4支相同鉛筆)
2個 3(想成2支相同鋼筆)
1個 5(想成1支原子筆)
例如:
x 得0個2 ，2個3，0個5
y 得3個2 ，0個3，0個5
z 得1個2 ，0個3，1個5
即表示 x=1×9x1=9, y=8×1x1=8, z=2×1x5=10，此時滿足 xyz=720
任意分給 x, y, z 三人(想成甲乙丙三人)，方法是
(2)在(1)的例子x=9, y=8, z=10，
當 x,y,z是整數，下面三個也是其解
(9,-8,-10), (-9,8,-10),(-9,-8,10)
所以答=270×4=1080
練習:
方程式 xyz=1800
(1)有幾組正整數解
(2)整幾組整數解
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