Question

用数学归纳法证明x^2n-1+y^2n-1能被x+y整除

Answer 1

当n=1时x^(2n-1)+y^(2n-1)=x+y(x+y)/(x+y)=1能被x+y整除.假设当n=k(k为整数,且k>=2)时,x^(2k-1)+y^(2k-1)能被x+y整除,则当n=k=1时令x^(2k-1)+y^(2k-1)=A(x+y)则x^(2k-1)=A(x+y)-y^(2k-1)x^[2(k+1)-1]+y^[2(k+1)-1]=x...