Consider the set $$M = \left\{\frac{a}{\overline{ba}}+\frac{b}{\overline{ab}} \, | a,b\in\{1,2,3,4,5,6,7,8,9\} \right\}.$$a) Show that the set $M$ contains no integer. b) Find the smallest and the largest element of $M$
Source: 2017 Romanian NMO grade VII P1
Tags: number theory, Digits
Consider the set $$M = \left\{\frac{a}{\overline{ba}}+\frac{b}{\overline{ab}} \, | a,b\in\{1,2,3,4,5,6,7,8,9\} \right\}.$$a) Show that the set $M$ contains no integer. b) Find the smallest and the largest element of $M$