So we can say, that if you can sign with (1LZtnC7Ck37V9uLGGXFmaVkeaLyzFLvf6W) then you have the private key of Satoshi's key.
Yeah. If you knew the private key of - 1LZtnC7Ck37V9uLGGXFmaVkeaLyzFLvf6W - you'd be one step far from calculating this sought after Satoshi's address. It's simple elliptic curve maths.
If
k1G + k2G = k3G then
(k1 + k2)G = k3G →
k1 + k2 = k3.
Beautiful, isn't it?