3.9

1. So when the author says to let x=y^(p+1)/4 (mod p) so that x^4=y^p+1 (mod p), do we know x and y?

2. While I was reading, I was thinking how the actual intuition behind Fermat's theorem has been kept from me in my education. I know proof techniques and enough number theory to justify it, but it has been so formalized that the impetus is lost. Then I started thinking, maybe results are what's important since they allow us to settle our brains--to rest them upon the rigor and irrefutable truth proof brings. We start thinking of things at higher levels and in more general terms until we're all brought up in the same education and creativity is only preserved in the sporadic genius of choice minds.