Ma458 Homework 5
This assignment is due next Thursday
(10/15) but start it over the weekend so we can discuss it some on
Read Chapters 12 and 14 in Silverman. (Note that I've skipped
13. There's some really interesting stuff there, but it's mostly
expository. There's little in it you can actually learn to
do in this course.
Silverman, Exercise 12.2. Part (a) is easy once you really understand the
proof of Theorem 12.2. When you write up your solution, try to copy
Silverman's writing style.
Part (b) is easy once you understand Silverman's argument showing that
Theorem 12.2 is false for primes congruent to 1 modulo 4.
Read Chapter 18 (yes, skip to 18) - to understand the general idea,
not the details. We'll go back to Chapters 16 and 17 for the
background we need for those details.
Be prepared to present two different proofs that there is no rational
number whose square is 2. (Note that this statement never uses the
words "square root". You proofs shouldn't either).
Use the strategy we developed in class today to study the diophantine
x2 - 3 y 2 = +- 1.
If you have the time and energy, think about
x2 - d y 2 = +- 1
for larger values of d.
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