Write the following numbers as a sum of two squares.. Write the following numbers as a sum of two squares:
$$(a) 13\times17$$
$$13\times17=221$$
$$m=13=(3^2+2^2) \space \text{and} \space n=17=(4^2+1^2)$$
$$[(3)(4)+(2)(1)]^2+[(3)(1)-(4)(2)]^2=14^2+(-5)^2=221$$
I had no problem solving this one.  However, the next problem is giving me trouble because $19^{10}$ is such a large number.
$$(b) 13\times19^{10}$$
$$13\times19^{10}=79703861351413$$  I can only find this number using wolfram.  My calculator wont display all the digits.  Which is a problem.
$$m=13=(3^2+2^2) \space \text{and} \space n=19^{10}=(c^2+d^2)$$
Is there a easy / simple method I can use to find $c$ and $d$?

Hint: 13=9+4, $19^{10} $  is a square.
