Re: [中學] 階乘問題方程式?

看板Math作者Honor1984 (希望願望成真)時間9年前 (2015/04/05 14:33)推噓2(2推 0噓 1→)

留言3則, 2人參與討論串2/2 (看更多)

※ 引述《ardenn (太陽)》之銘言： : 五個正整數a,b,c,d,e 且 a*b*c*d*e=9! abcde = 2^7 * 3^4 * 5 * 7 : 又滿足四個方程式 : a*b+a+b = 524 (a + 1)(b + 1) = 525 = 3 * 5^2 * 7 -------- (1) : b*c+b+c = 146 (b + 1)(c + 1) = 147 = 3 * 7^2 --------(2) : c*d+c+d = 104 (c + 1)(d + 1) = 105 = 3 * 5 * 7 : d*e+d+e = 149 求 a+b+c+d+e = ? (d + 1)(e + 1) = 150 = 2 * 3 * 5^2 ---------- (2) (a + 1)(e + 1)[(b + 1)(c + 1)(d + 1)]^2 = 2 * 3^4 * 5^5 * 7^4 2 * 5 | (a + 1)(e + 1) 由(1)知5^2 | (a + 1) => 2 | (e + 1) (b + 1) = 3 * 7 => b = 20 a + 1 = 25 => a = 24 c + 1 = 7 => c = 6 d + 1 = 15 => d = 14 e + 1 = 10 => e = 9 : 感謝!! b(a + c) + (a + 2b + c) = b(a + c + 2) + (a + c) = 670 => b(a + c) = 335 同理 2c(b + d) = 250 => c(b + d) = 125 2d(c + e) = 253 => d(c + e) = -- ※ 發信站: 批踢踢實業坊(ptt.cc), 來自: 61.228.134.164 ※ 文章網址: https://www.ptt.cc/bbs/Math/M.1428215618.A.517.html

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Honor1984

04/05 14:37, , 1^F

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ardenn

04/05 14:44, , 2^F

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ardenn

04/05 15:08, , 3^F

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