Correcting another couple of errors issued by Emanuele.

book/library.bib

@@ -27,9 +27,17 @@
   year = {2001}
 }
 
+@misc{rfc6176,
+  title = {Prohibiting Secure Sockets Layer (SSL)
+           Version 2.0},
+  author = {S. Turner and T. Polk},
+  publisher = {RFC Editor},
+  url = {http://tools.ietf.org/html/rfc6176}
+}
+
 @book{bombelli:algebra,
   title = {L'Algebra},
-  author ={Rafael Bombelli},
+  author = {Rafael Bombelli},
   year={1572},
   url={http://mathematica.sns.it/opere/9/}
 }
@@ -72,7 +80,7 @@
  address = {Cambridge, MA, USA},
 }
 
-@book{Crandall:,
+@book{Crandall,
     author = {Richard Crandall and Carl Pomerance and Richard Crandall and Carl Pomerance},
     title = {Prime numbers: a computational perspective. Second Edition},
     year = {2005}
@@ -86,4 +94,36 @@
  volume = {36},
  pages = {553--558},
  url = {http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.92.5261}
+}
+
+
+@article{pollard1974,
+ author = {J. M. Pollard},
+ title = {Theorems on factorization and primality testing},
+ journal = {Mathematical Proceedings of the Cambridge Philosophical Society},
+ volume = 76,
+ issue = 03,
+ month = 11,
+ year = 1974,
+ issn = {1469-8064},
+ pages = {521--528},
+ numpages = 8,
+ doi = {10.1017/S0305004100049252},
+ url = {http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=2074504}
+}
+
+
+@article{William:p+1,
+  title = {A $p + 1$ Method of Factoring},
+  author = {Williams, H. C.},
+  journal = {Mathematics of Computation},
+  volume = 39,
+  number = 159,
+  jstor_formatteddate = {Jul., 1982},
+  pages = {pp. 225-234},
+  url = {http://www.jstor.org/stable/2007633},
+  ISSN = 00255718,
+  language = {English},
+  year = 1982,
+  publisher = {American Mathematical Society},
 }

book/math_prequisites.tex

@@ -14,6 +14,8 @@ The logarithmic $\log$ function is assumed to be in base two, i.e. $\log_2$.
 \\
 The $\idiv$ symbol is the integer division over $\naturalN$, i.e.
 $a \idiv b = \floor{\frac{a}{b}}$.
+\\
+$\naturalPrime \subset \naturalN$ is the set containing all prime intgers.
 
 \section{Algorithmic Complexity Notation}
 The notation used to describe asymptotic complexity follows the $O$-notation,
@@ -72,8 +74,8 @@ Anyway, both show that algorithm ~\ref{alg:gcd} belongs to the class
 
       \Else
         \If{$b$ is odd}
-          \State $a = a \gg 1$
-          \If{$a < b$} $a, b = b, a$ \EndIf
+          \State $a \gets a \gg 1$
+          \If{$a < b$} $a, b \gets b, a$ \EndIf
         \Else
           \State $k \gets k+1$
           \State $a, b \gets a \gg 1, b \gg 1$
@@ -157,7 +159,17 @@ for completeness' sake, we report in table
 
 For each digit of the result, we perform a subtraction, and a limited number of
 multiplications. This means that the complexity of this solutions belongs to
-\bigO{\log n \log n} = \bigO{\log^2 n}
+\bigO{\log n \log n} = \bigO{\log^2 n}.
+
+\begin{remark}
+  Note that Bombelli actually has found a solution in $x$ for a slightly
+  different equation than the one we initially formulated. Specifically, he
+  found the pair $\angular{x, r}$ such that $(x+r)^2=a$, where $x$ is the mantissa,
+  while $r$ is the decimal part. For our purpose this change is irrelevant: we
+  just need to be able to distinguish perfect squares, and thus assert that $r$
+  is nonzero.
+\end{remark}
+
 \paragraph{Dijkstra's Algorithm \label{par:preq:sqrt:dijkstra}} can be found in
 \cite{Dijkstra:adop}, \S 8, p.61. There, Dijkstra presents an elightning
 process for the computation of the square root, making only use of binary shift
@@ -213,7 +225,7 @@ For any further details and explainations, the reference is still
 \begin{algorithm}[H]
   \caption{Square Root: final version}
   \label{alg:sqrt:dijkstra}
-  \begin{algorithmic}
+  \begin{algorithmic}[1]
     \State $p, q, r \gets 0, 1, n$
     \While{$q \leq n$} $q \gets q \gg 2$ \EndWhile
     \While{$q \neq 1$}

book/question_authority.tex

@@ -128,6 +128,8 @@
     its results in algebraical notation, were provisions made accordingly.}
          {Augusta Ada, Countess of Lovelace}
 
+
+%% there is no copyright, but the right to copy.
 \begin{figure}[b]
   \centering
   \includegraphics[width=80pt]{kopimi.png}