整数x ,y,z满足(x-y)(y-z)(z-x)=x+y+z.证明:x+y+z能被27整除一道属于整除性的问题

已知整数x,y,z满足(x-y)(y-z)(z-x)=x+y+z,证明:x+y+z是27的倍数 已知整数x、y、z,满足x≤y＜z,且｜x+y｜+｜y+z｜+｜z+x｜=4,｜x-y｜+｜y-z｜+｜z-x｜=2,求x^2+y^2+z^2的值. 整数x、y、z满足x≤y＜z|x+y|+|y+z|+|z+x|=4|x-y|+|y-z|+|z-x|=2求x²+y²+z² 已知整数x,y,z满足x≤y＜z,且|x+y|+|y+z|+|z+x|=4 |x-y|+|y-z|+|z-x|=2 那么x²+y²+z²的值 满足（y+z)^2011+(z+x)^2011+(x+y)^2012=2的整数组（x,y,z)有几组? 你能找出三个整数 x,y 和z,满足 (x+y+z)^3= 设x,y,z为整数且满足|x-y|^2001+|z-x|^2002=1,求|x-y|^3+|y-z|^3+|z-x|^3的值? 设整数x,y,z满足(x-y)(y-z)(z-x)=x+y+z,证明：27|（x+yz+）. 求所有三元组(x,y,z),满足x,y,z是正有理数,且x+1/y,y+1/z,z+1/x都是整数. 已知x,y,z均为整数并满足{|x+y|+|y+z|+|z+x|=2} {|x-y|+|y-z|+|z-x|=2} 求x+y^2+z^3的值 设XZY是整数,且满足(X-Y)(Y-Z)(Z-X)=X+Z+Y 试证明X+Y+Z能被27整除设XZY是整数,且满足(X-Y)(Y-Z)(Z-X)=X+Z+Y 试证明X+Y+Z能被27整除 若整数x,y,z满足(15/8)^x*(16/9)^y*(27/10)^z=16,求(7x+y)/(z-y)的值. 整数x ,y,z满足(x-y)(y-z)(z-x)=x+y+z.证明:x+y+z能被27整除一道属于整除性的问题 x-y/(z-x)(z-y) 一y-z/(x-y)(x-z) ＋z-x/(y-z)(y-x) x^-(y-z)^/(x+y)^-z^ 计算（x+y-z)(x-y-z) 计算：(x-y+z)(-x+y+z) (x+y-z)(x-y+z)=