Diff for "factorization_of_integers_of_special_forms"

Differences between revisions 1 and 20 (spanning 19 versions)

factorization_of_integers_of_special_forms (last edited 2008-11-14 13:41:51 by anonymous)

-  ⇤ ← Revision 1 as of 2007-01-23 01:39:03 → 
  Size: 71
  Editor: TimothyClemans
  Comment:
+   ← Revision 20 as of 2007-01-24 05:36:02 → ⇥
  Size: 989
  Editor: TimothyClemans
  Comment:
-Deletions are marked like this.
+Additions are marked like this.
 Line 1:
-* 2^n-1 where n is odd 
* 2^n+1 where n is odd
* 2^n+1 where n=4k-2
+ *  $a^{n} \pm 1$  for  $a = 2, 3, 5, 6, 7, 10, 11, 12$  and large exponents n [http://homes.cerias.purdue.edu/~ssw/cun/index.html]
 *  $a^{n} \pm 1$  for  $a \leq 13$  and  $a$  not a perfect number [http://wwwmaths.anu.edu.au/~brent/factors.html]
 *  $2^{n} \pm 1$  for  $1200 < n < 10000$  [http://www.euronet.nl/users/bota/medium-p.htm]
 *  $10^{n} \pm 1$  for  $n \leq 100$  [http://www.swox.com/gmp/repunit.html]
 *  $p^{p} \pm 1$  where  $p$  is a prime number and  $p < 180$ . [http://homes.cerias.purdue.edu/~ssw/bell]
 *  $2^{2^{n}} + 1$  (Fermat numbers) [http://www.prothsearch.net/fermat.html]
 *  $2^{3^{n}} \pm 1$  [http://www.alpertron.com.ar/MODFERM.HTM] 
 * Fibonacci numbers ( $F_{n}$ ) and Lucas numbers ( $L_{n}$ ) for  $n < 10000$  [http://home.att.net/~blair.kelly/mathematics/fibonacci/]
 *  $n * 2^{n} \pm 1$  (Cullen and Woodall numbers) [http://www.leyland.vispa.com/numth/factorization/cullen_woodall/cw.htm]
 * Euclid numbers [http://en.wikipedia.org/wiki/Sylvester's_sequence#Divisibility_and_factorizations]