Question

用数学归纳法证明:x^(2n+1)+y^(2n+1)能被x+y整除

Answer 1

n=0时肯定成立了,现在n-1时结论成立,看n的情形；x^(2n+1)+y^(2n+1)=x^(2n+1)+x^(2n)*y+xy^(2n)+y^(2n+1)-x^(2n)*y-xy^(2n)=(x^(2n)+y^(2n))(x+y)-(x^(2n-1)+y^(2n-1))xy等式的后半部分(x^(2n-1)+y^(2n-1))xy根据归纳...