COMPUTER PROBLEMS:
DAY 10
(1) Find the first 10,000 pythagorean triples.
(2) Find integral solutions to y 2 = x3 + 17. (It is known that eight such solutions
exist.)
(3) Find rational points of y 2 = x3 + 17.
(4) We can look for pairs of integers that are solutions to the elliptic curve y 2 =
x3 + ax + b modulo a prime p. Write a Python program that prints out all
such solutions for a specificied curve and prime p.
(5) Yesterday in class, we discussed the group law that allows points on elliptic
curves to be added. On the website, follow the link elliptic curve group law in
Python. Experiment with this code. You may also want to try the code there
that uses elliptic curves to factor large numbers.
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