16.3, due on November 30

1. (Difficult): How is elliptic curve factoring like the p-1 factoring algorithm?

And why do we have to invert 599 when computing 8*7!?

And 8!P is not equal to infinity mod 761 because 8! is not a multiple of 777, but why must only multiples of 777 give inifinity mod 761 again; how is this related to cycles mod any number? I need to understand this example (starting on page 357) better to understand the general case I think.

And I have lots of questions about singular curves, so I'll just be brief and say I didn't really understand singular curves.

2. (Reflection): The elliptic curve factorization method seems pretty strong.

Also, so addition and multiplication on using points on an elliptic curve is analogous to multiplication and exponentiation using modular arithmetic. I think that's what the book is saying.

The last statement I think is a cool discovery that the p-1 and division trial methods are both encompassed by the elliptic curve factorization method. (360)