I need opinions

In a bible study I lead, we recently discussed Matthew ch. 4 and the temptation narrative. Some time ago I came to the conclusion that satan must not know that Jesus was God. Why? First and most important, it is impossible for Jesus--being God--to sin; it is metaphysically impossible. If satan knew that Jesus was God, he would be aware of this, and wouldn't even have bothered.

Also, the fact that satan refers to Jesus as "Son of God" does not indicate that he knows Jesus is the Son of God, in that the title was used on numerous occasions in the OT to refer to human beings, individually and collectively.

Furthermore, there is no evidence that satan believed that Jesus was God, so why argue in favor of it?

Well, a number of people I've talked with have done just that, much to my amazement. I'm wondering if my friends in blogland can help. What do you think? In the desert, did satan know that Jesus Christ was God Almighty?