A number theory problem by MaFiA maNiAc

$N=\overline{7AB73}$

If $N$ is divisible by 99 then it is divisible by 9 and 11

For divisible by 11 it should satisfy :

$(7+B+3)-(A+7)=11 k$

$k$ can be $0,1$

For divisibility by 9 it should satisfy:

$9| 7+A+B+7+3=17+A+B=18 +A+B-1$

it implies that $9|A+B-1$

If $k=0$

$B-A+3=0$

$A=B+3$

Usong this in second part $9|B+3+b-1$

$9|2(B+1)$ It has no solution

Now for $k=1$

$B-A+3=11$

$B=A+8$

Putting this in secon part

$9|2 A +7$

it has only one solution $A=1$ and $B=9$