用数学归纳法证明命题当N为正奇数时
用数学归纳法证明命题“当N为正奇数时,x的n次方+y的n次方能被x+y整除.”
涂建平回答:
当n=1时x+y能被x+y整除当n=3时x^3+y^3=(x+y)(x^2-xy+y^2)能被x+y整除假设当n=2k-1时x^(2k-1)+y^(2k-1)能被x+y整除和当n=2k+1时x^(2k+1)+y^(2k+1)能被x+y整除当n=2k+3时x^(2k+3)+y^(2k+3)=[x^(2k+1)+y^(2k+1)](x^...
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用数学归纳法证明命题当N为正奇数时
用数学归纳法证明命题“当N为正奇数时,x的n次方+y的n次方能被x+y整除.”
涂建平回答:
当n=1时x+y能被x+y整除当n=3时x^3+y^3=(x+y)(x^2-xy+y^2)能被x+y整除假设当n=2k-1时x^(2k-1)+y^(2k-1)能被x+y整除和当n=2k+1时x^(2k+1)+y^(2k+1)能被x+y整除当n=2k+3时x^(2k+3)+y^(2k+3)=[x^(2k+1)+y^(2k+1)](x^...