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百鸡问题
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百鸡问题
bǎi jī wèn tí
中国古代著名算题。原载《张邱建算经》卷下第三十八题:“今有鸡翁一值钱五,鸡母一值钱三,鸡雏三值钱一。凡百钱买鸡百只,问鸡翁、母、雏各几何?”如设鸡翁数为x,鸡母数为y,鸡雏数为z,就可得一次不定方程组:x+y+z=100,5x+3y+13z=100。原书虽列出全部三组正整数答案:4,18,78、8,11,81、12,4,84,但对解法根据没有详述。后世很多人研究此题,并各自得出解法,称为“百鸡术”。
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