The set off

a = r_{k}, b = r_{k+1},

redefines a and b. Instead use the following argument:

Suppose r_{n} is the last nonzero element of the sequence, so r_{n+1} = 0, then by Theorem 1.8.1 and the definition of the sequence,

gcd(a, b) = gcd( r_{0}, r_{1}) = gcd(r_{k}, r_{k+1}), k = 1, 2, ... n.

At the last step we have

gcd(a, b) = gcd(r_{n}, 0) = r_{n}.

This is what is returned by the gcd algorithm.

a = r

redefines a and b. Instead use the following argument:

Suppose r

gcd(a, b) = gcd( r

At the last step we have

gcd(a, b) = gcd(r

This is what is returned by the gcd algorithm.

Page 21: The label (1.12) should be moved up to the previous equation.

Page 58: Errata entry for page 59 is on page 58.

Page 68: Errata should refer to 2.23.12 not 2.22.12

Page 117: Second entry in Errata for that page should not refer to p. 105.

Page 168: Errata should refer to Example 8.3.1 not 7.2.1. Ignore the sentence fragement starting wih p. 145....

Page 171 Errata, Second error listed: Page number is wrong - no idea?

Page 274: Errata for page 279 should be for this page. Also 1ßpmod4 appears to be a typo in the replacement problem. 1 mod 4 ??