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set loopTimes to choose from list {"1", "2", "3", "4", "5", "6", "7", "8", "9", "10"} with prompt "Open this many TextEdit documents:" tell the application "TextEdit" end tell

Multiplying all the numbers in each representation then gives 6! 3 6 6! (mod 7), and dividing by 6! we get 36 1 (mod 7), exactly the result we wanted in the case a = 3, p = 7 Now let s generalize this argument to other values of a and p, with S = {1, 2, , p 1} We ll prove that when the elements of S are multiplied by a modulo p, the resulting numbers are all distinct and nonzero And since they lie in the range [1, p 1], they must simply be a permutation of S The numbers a i mod p are distinct because if a i a j (mod p), then dividing both sides by a gives i j (mod p) They are nonzero because a i 0 similarly implies i 0 (And we can divide by a, because by assumption it is nonzero and therefore relatively prime to p) We now have two ways to write set S: S = {1, 2, , p 1} = {a 1 mod p, a 2 mod p, , a (p 1) mod p} (p 1)! ap 1 (p 1)! (mod p)

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A classic example of passing session state through the URL is the Report and Form on a Table generated by a wizard within APEX The wizard builds a report page that shows the rows in a database table with an edit link next to each row When users click on the edit link they are taken to the form page where they can edit the data in that row, as shown in Figure 12-8 The primary key of the table is passed as a parameter in the URL The query on the form page uses that primary key as a query predicate to select the desired row In our example, what would happen if a user simply changed the value of the primary key in the URL (aka URL tampering) If the user chose a value that matched another row in the table, that row would appear in the form This raises an obvious security concern as end users are able to change the value used in the query predicate at will Imagine now that the developer in this example wanted to limit the rows a user could edit by simply limiting the rows shown on the report page If there is no row to click, how can a user edit that row This false assumption by a developer could easily allow a user to gain access to data he or she is not supposed to see The first instinct of many developers is to make the request an HTTP POST instead of a GET, as the value is not passed through the URL The reality is that this technique is simply security through obscurity Many web developer tools are available that allow an end user to view and manipulate post data or simply turn the POST into a GET To address these concerns, APEX offers several new features that let developers easily protect their applications against such threats.

6 Add the repeat times loop within the tell block, as shown in boldface here:

Dividing by (p 1)! (which we can do because it is relatively prime to p, since p is assumed prime) then gives the theorem This theorem suggests a factorless test for determining whether a number N is prime: 31

In many scenarios, certain application- or page-level items should never be set by an end user Suppose, for example, that the end user s role, such as Administrator or Guest, is stored in an application-level item If an end user can change the value of this item, she could gain access

set loopTimes to choose from list {"1", "2", "3", "4", "5", "6", "7", "8", "9", "10"} with prompt "Open this many TextEdit documents:" tell the application "TextEdit" repeat loopTimes times make new document at the front end repeat end tell

Figure 17 An algorithm for testing primality function primality(N ) Input: Positive integer N Output: yes/no Pick a positive integer a < N at random if aN 1 1 (mod N ): return yes else: return no

FIGURE 12-8

the choose from list dialog box, click the OK button, and verify that TextEdit creates the number of documents you chose

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