How do you write $7 \cdot 10^{100} +7$ as a sum of four squares?
I know that you can write it as a sum of four squares by the Lagrange's Four Squares Theorem, but I don't know how to write such a big number as a sum of four squares. I've tried writing $10^{100}$ as ${(10^{50})}^2$ or as $10^{10} \cdot 10^{10} \cdot 10^{10} \cdot 10^{10} \cdot 10^{10} \cdot 10^{10} \cdot 10^{10} \cdot 10^{10} \cdot 10^{10} \cdot 10^{10} \cdot$ and then work it out but it didn't seem to help.