求X平方加y平方等于Z平方的所有整数解
x\u7684\u5e73\u65b9\u52a0y\u7684\u5e73\u65b9\u7b49\u4e8e204 \u6c42x.y\u7684\u6574\u6570\u89e3 \u8c22\u8c22\u4e86\u90ed\u6566\u9852\u56de\u7b54\uff1a
x²+y²=204\uff0c\u6c42x\u4e0ey\u7684\u6574\u6570\u89e3\u3002
\u5148\u5728\u5b9e\u6570\u5185\u6c42\u89e3\uff0c\u56e0204\u4e0d\u5927\uff0c\u6545\u7528\u9010\u4e00\u9a8c\u7b97\u6cd5\uff0c
x²\uff0cy²\u7684\u7ed3\u679c\uff1a1\uff0c203\u4e0d\u662f\uff1b4\uff0c200\u4e0d\u662f\uff1b9\uff0c195\u5426\uff1b16\uff0c188\u5426\uff1a25\uff0c179\u5426\uff1b36\uff0c168\u5426\uff1b49\uff0c155\u5426\uff0c64\uff0c140\u5426\uff0c81\uff0c123\u5426\uff0c100\uff0c104\u5426\uff0c
\u5b9e\u6570\u5185\u65e0\u6574\u6570\u89e3\u3002
\u5373\u4fbf\u5728\u590d\u6570\u5185x\u4e0ey\u4e5f\u65e0\u6574\u6570\u89e3\u3002
\u82e5xy=2\u221a51\uff0c
\u2234xy=2\u221a51=2\u00d7\u221a3\u00d7\u221a17\uff0c
\u2234\u5bf9\u4e8exy=2\u221a51\uff0c\u6700\u591a\u6709\u4e00\u4e2a\u6574\u65702\u62161\uff08\u6216\uff0d2\uff0c\uff0d1\uff09\u662f\u5b83\u4ed6\u4eec\u7684\u6574\u6570\u89e3\uff0c\u800c\u7edd\u65e0\u4e24\u4e2a\u6574\u6570\u89e3\u3002
\u9525\u9762 \u5750\u6807\u539f\u70b9\u4e3a\u9876\u70b9
(3,4,5)(5,12,13)
(7,24,25)
(6,8,10)
(8,15,17)
(10,24,26)
(12,35,37）
(8,15,17)
(12,35,37)
(16,63,65)
x²+y²=z²
x=3，y=4，z=5
x=6，y=8，z=10
x=5，y=12，z=13
......
有无数组解.
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绛旓細(3,4,5)(5,12,13)(7,24,25)(6,8,10)(8,15,17)(10,24,26)(12,35,37锛(8,15,17)(12,35,37)(16,63,65)
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绛旓細X = P锛2 + PQ锛X绛変簬P骞虫柟鍔PQ锛塝 = Q锛2/ 2 + PQ锛Y绛変簬浜屽垎涔婹鏂瑰姞PQ锛塟 = P锛2 + Q锛2 / 2 + PQ锛Z绛変簬P骞虫柟鍔犱簩鍒嗕箣Q鏂瑰姞PQ锛6锛 姝ゅ叕寮忔兜鐩栦簡鑷劧鐣岀殑鍏ㄩ儴鍕捐偂鏁帮紝鍖呮嫭娲剧敓鍕捐偂鏁般7锛 鐢ㄦ鍏紡寰堝鏄撳鍑哄叏閮ㄥ嬀鑲℃暟锛屼緥濡2000浠ュ唴鐨勫嬀鑲℃暟璁℃湁320缁...
绛旓細鐢ㄧ悆鍧愭爣 鈭埆鈭垰(x^2+y^2+z^2)dxdydz =鈭埆鈭 r*r²sin蠁 drd蠁d胃 =鈭玔0--->2蟺] d胃鈭玔0--->蟺] sin蠁d蠁鈭玔0--->鈭2] r³ dr =2蟺(-cos蠁)(1/4)r⁴ 蠁锛歔0--->蟺],r锛歔0--->鈭2]=4蟺 ...
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