Assignment, Week 2

Reading in Silverman

Chapter 3: Pythagorean Triples and the Unit Circle
Chapter 4: Sums of Higher Powers and the Fermat Theorem
Chapter 5: Divisibility and the Greatest Common Divisor
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Chapter 4 is mostly historical.

Problems

A Problems

2.1, 2.2, 2.3
3.1
5.1
Notes. Problems 2.1. 2.3, and 3.1 explore the properties of Pythagorean triples. Problem 5.1 introduces you to an efficient way of finding greatest common divors (gcd's). For example gcd(15,10) = 5, gcd(3,7) = 1. We'll use the gcd and the Euclidean algorithm used to compute it over and over again. Learn the gcd well!

B Problems

Second Edition: I suggest looking at 3.2, 3.3, 3.4. You can also try 4.1 and 4.2.
Problem 4.1 is of a different character, and is recommended:
It is a short historical essay.
First Edition: Instead look at ch 3: problems A.3.1, A.3.2. ch 4: problems 4.1 and A.4.1. (See page 247, "A" stands for "additional problems")

Primitive Pythagorean Triples

3, 4, 5
5, 12, 13
7, 24, 25
8, 15, 17
9, 40, 41
11, 60, 61
12, 35, 37
13, 84, 85
15, 112, 113
16, 63, 65
17, 144, 145
19, 180, 181
20, 21, 29
20, 99, 101
24, 143, 145
28, 45, 53
28, 195, 197
33, 56, 65
36, 77, 85
39, 80, 89
44, 117, 125
48, 55, 73
51, 140, 149
52, 165, 173
57, 176, 185
60, 91, 109
65, 72, 97
85, 132, 157
88, 105, 137
95, 168, 193
104, 153, 185
119, 120, 169