0≤a,b≤9⇒−9≤a−b≤9;a+b≤18

We have 53ab98¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯⋮99

,so :

+ 53ab98¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯⋮9⇒25+a+b⋮9⇒a+b=2;11

+53ab98¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯⋮11⇒|5+a+9−3−b−8|=|3+a−b|⋮11

⇒a−b=−3;8

If a + b = 2,then a + b is even but 2b is even

=> a + b - 2b = a - b is even => a - b = 8 > a + b (absurd)

=>{a+b=11a−b=−3⇒{2a=8b=11−a

⇒{a=4b=7

\(0\le a,b\le9\Rightarrow-9\le a-b\le9;a+b\le18\)

We have \(\overline{53ab98}⋮99\),so :

+ \(\overline{53ab98}⋮9\Rightarrow25+a+b⋮9\Rightarrow a+b=2;11\)

+\(\overline{53ab98}⋮11\Rightarrow\left|5+a+9-3-b-8\right|=\left|3+a-b\right|⋮11\)

\(\Rightarrow a-b=-3;8\)

If a + b = 2,then a + b is even but 2b is even

=> a + b - 2b = a - b is even => a - b = 8 > a + b (absurd)

=>\(\left\{{}\begin{matrix}a+b=11\\a-b=-3\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}2a=8\\b=11-a\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}a=4\\b=7\end{matrix}\right.\)