Assignment 1--due July 1

Laubenbacher and Pengelly, Chapter
4, Exercises 4.3, 4.5, 4.7, 4.8

Hint for 4.8: Any odd number can be
written as 2n + 1. Show that its square is then of the form 4m + 1. Show
that any square of an even number must be of the form 4q. What about the
sum of two odd squares?

Exercise 4.9. Then use the Euclidean algorithm to find which primitive Pythagorean triples are associated with these triples.

(a) (85, 204, 221)

(b) (231, 392, 455)

(c) (57, 176, 185)