Determine all three-digit number ,##N##, having the property that ##N## is divisible by 11, and ##\frac{N}{11}## is equal to the sum of the square of the digits of ##N##.(adsbygoogle = window.adsbygoogle || []).push({});

This cannot be solved just by guessing. I think I should use mathematica for this,but, this sum of the digits is a scary thing. Does mathematica has a feature for that?

I know that

-##N## is a multiple of 11.

Let the digits of ##N## be ##a,b \text{ and } c## respectively.

Now, ##11(a^2+b^2+c^2)=abc##

I can't think of a way.

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# [Mathematica] Number problem with digits

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