1.反例:ab=12 12:21 =/= 2:3
2.ab 是 9的倍数,a+b=18 或 a+b=9
如 a+b=18,此数为 99,a=9,b=9,很容易证明.
如 a+b=9 ===> (a-b)[9-(a+b)]=0 ===>
(a-b)(10-a-b-1)=0 ===>
10a - 10b + b^2 - a^2 + b - a = 0 ===>
10a + b^2 + b = 10b + a^2 + a ===>
10a*b + 10a + b^2 + b = 10a*b + 10b + a^2 + a ===>
(10a+b)/(10b+a) = (a+1)/(b+1)
证毕.