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496 24 (25 2 1) 8128 26 (27 21). The perfect numbers listed above are all even; it is not known if odd perfect numbers exist. In the third century B.C ., Euclid proved that if p and 2p 2 1 are prime, then 2p21(2p 2 1) is perfect. Euler proved in the eighteenth century that every even perfect number was of this form. Marin Mersenne (1588 1648) was a monk in the Order of Minims near Paris. He taught philosophy and was interested in science and mathematics. If 2n 21 (n . 2) is a prime, then n must be a prime; for if N st, then 2st21 (2s 2 1) (2s(t21) 2s(t22) 1). In 1644 Mersenne conjectured that 2p 2 1 is a prime for p 2, 3, 5, 7, 13, 17, 19, 31, 67, 127, 257 and these were the only solutions for p 257. It is unlikely that Mersenne could have tested all of these numbers in 1644 and his conjecture is not completely correct. Table 13.14 lists 43 known Mersenne numbers, the last discovered on December 15, 2005, by Dr Curtis Cooper and Dr Steven Boone, professors at Central Missouri State University. The table includes the value of p(Mp 2p 2 1), the year of the discovery of Mp, and the number of digits D(Mp) in Mp.

The primary differences pertain, as you might expect, to the server-oriented nature of the page. As noted in the fourth step, you ll need to remove all HTML from your application page. This is a necessary action because the full XSLT page already contains the HTML framework <html>, <head>, and <body> tags and to leave it in the application page would cause errors. Another difference is the manner in which the XSLT page is connected to the data. Rather than link to the XSLT page from the XML file, you apply a Dreamweaver server behavior in the dynamic page to create a connection to the XSLT file and its related XML data. To link to the full XSLT page from the dynamic page, follow these steps:

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in the production of nitrous oxide. Soil Biol. Biochem. 33:1723 1732. Xiao, S., D.W. Kicklighter, J.M. Melillo, A.D. McGuire, P.H. Stone, and A.P. Sokolov. 1997. Linking a global terrestrial biogeochemical model and a 2-dimensional climate model: implications for the global carbon budget. Tellus 49B:18 37. Yock, D.C. 2002. Dimethylsulfonioproprionate: its sources, role in the marine food web, and biological degradation to dimethylsul de. Appl. Environ. Microbiol. 68:5804 5815. Zabel, R.A. and J.J. Morrell. 1992. Wood Microbiology: Decay and its prevention. Academic Press, San Diego, CA. Zahrl, D., M. Wagner, K. Bischof, et al. 2005. Peptidoglycan degradation by specialized lytic transglycosylases associated with type III and type IV secretion systems. Microbiology 151:3455 3467. Zehnder, A.J.B. and T.D. Brock. 1979. Anaerobic methane oxidation: occurrence and ecology. Appl. Environ. Microbiol. 39:194 204.

A custom function using tail recursion is designed to complete all its work at each call so that nothing need be held in memory while subsequent calls are evaluated. To do so, the function must be structured to pass its result to the next call (via the defined parameters or via a variable) rather than holding it on the stack.

1. Select the image you want to crop. 2. In the Property inspector, click the Crop button. 3. Dreamweaver displays an alert to warn you that the cropping operation changes the selected image; click OK to clear the dialog. A shaded border appears within the selected image (see Figure 9-8).

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