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20 0 4年 1月号问题解答(解答由问题提供人给出 )1 471 求方程组 x+y =ztz+t =xy的非负整数解 .解 因为方程组中x与y ,z与t可以互换 ,所以可以先求满足 0 ≤x≤y ,0 ≤z≤t的整数解组 (x,y ,z,t) .( 1 )若x、z中有一个为零 ,不妨设x=0 ,则由原方程组消去t得 :y+z2 =0所以y =z
January 2004 Issues Issued January 2011 (Solution given by the problem provider) 1 471 Find a nonnegative integer solution to the system of equations x+y = ztz+t = xy. Solution Because x and y, z and t in the system of equations Can be interchangeable, so we can first find the integer unwrapping satisfying 0 ≤ x ≤ y, 0 ≤ z ≤ t (x, y, z, t). (1) If there is a zero in x, z, we can set x =0, then the original equations are eliminated t: y+z2 =0 so y=z