Determine all three-digit numbers
![N](/media/m/f/1/9/f19700f291b1f2255b011c11d686a4cd.png)
having the property that
![N](/media/m/f/1/9/f19700f291b1f2255b011c11d686a4cd.png)
is divisible by 11, and
![\dfrac{N}{11}](/media/m/d/b/5/db5f8e1e6a5a5bef35e116672f52dcb9.png)
is equal to the sum of the squares of the digits of
![N](/media/m/f/1/9/f19700f291b1f2255b011c11d686a4cd.png)
.
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Determine all three-digit numbers $N$ having the property that $N$ is divisible by 11, and $\dfrac{N}{11}$ is equal to the sum of the squares of the digits of $N$.