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[例1]求方程17(xyzt+xy+xt+zt+1) -54·(yzt+y+t)=0的正整数解. 解:原方程变形为:(xyzt+xy+xt+zt+1)/(yzt+y+t)=(54)/(17)把两边分别展开成连分数,即:
[Example 1] Find the positive integer solution of Equation 17 (xyzt+xy+xt+zt+1) -54(yzt+y+t)=0. Solution: The original equation is transformed into: (xyzt+xy+xt+zt) +1)/(yzt+y+t)=(54)/(17) Expand the two sides into consecutive scores, namely: