# Sum Cool Squares.

Number Theory Level 4

There exists two 4-digit numbers $$\overline{abcd}$$ such that $\overline{ab} ^{2} + \overline{cd} ^{2} = \overline{abcd}.$ What is the sum of those two numbers?

Note:
$${a,b,c,d}$$ are digits, not factors of a product.
$$a \neq 0$$.
Also, this problem is not original.

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