4. Determine the two-digit natural numbers for which the remainder of the division by 13 is equal to the quotient of the division by 11, and the remainder of the division by 11 is equal to the quotient of the division by 13.
Rezolvare.................

.1 p

Let x be the number we are looking for. We have $x=13 a+b$ and $x=11 b+a$

Then $13 a+b=11 b+a$ and we get $6 a=5 b$

Since $a$ is divisible by 5 and $a<8$, the number we are looking for is obtained for .a.न.5. şi.. $b .=.6 . . . . . . . . . . . . .3 . p$.

So $x=13 \cdot 5+6=11 \cdot 6+5=71$

$3 \mathbf{p}$