Diff for "factorization_of_integers_of_special_forms"

Differences between revisions 5 and 6

bn±1 for b=2,3,5,6,7,10,11,12 and large exponents n [http://homes.cerias.purdue.edu/~ssw/cun/index.html]
an±1 for a≤13 and a not a perfect number [http://wwwmaths.anu.edu.au/~brent/factors.html]

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

-  ⇤ ← Revision 5 as of 2007-01-23 02:41:17 → 
  Size: 1759
  Editor: TimothyClemans
  Comment:
+   ← Revision 6 as of 2007-01-23 02:43:56 → ⇥
  Size: 236
  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
 *  $2^{n} + 1$  where n = 4k
 *  $3^{n} - 1$  where n is odd      n < 540  .....      .........          . . . . 60
                   n ≤ 540             n = 6k − 3 ≤ 1077
 *  $3^{n} + 1$                        L, M for                    . . . . 66
 *  $5^{n} - 1$  where n is odd                 L, M for n = 10k − 5 ≤ 745 . . . .
                   n < 375                                         86
                   n ≤ 375
 *  $5^{n} + 1$                      ..................                     94
 *  $6^{n} - 1$  where n is odd      n < 330  . . . . . . . . . . . . . . . . . . 102
                   n ≤ 330    L, M for n = 12k − 6 ≤ 654 . . . . 106
 *  $6^{n} + 1$ 
 *  $7^{n} - 1$  where n is odd      n < 300  . . . . . . . . . . . . . . . . . . 116
                   n ≤ 300    L, M for n = 14k − 7 ≤ 595 . . . . 120
 *  $7^{n} + 1$ 
 *  $10^{n} - 1$  where n is odd      n < 330  .....      .........          . . . . 129
                   n ≤ 330             n = 20k − 10 ≤ 650
 *  $10^{n} + 1$                        L, M for                    . . . . 133
 *  $11^{n} - 1$  where n is odd      n < 240  .....      .........          . . . . 142
                   n ≤ 240             n = 22k − 11 ≤ 473
 *  $11^{n} + 1$                        L, M for                    . . . . 145
 *  $12^{n} - 1$  where n is odd      n < 240  .....      .........          . . . . 152
                   n ≤ 240             n = 6k − 3 ≤ 477 .
 *  $12^{n} + 1$                        L, M for                    . . . . 155
+ *  $b^{n} \pm 1$  for  $b = 2, 3, 5, 6, 7, 10, 11, 12$  and large exponents n [http://homes.cerias.purdue.edu/~ssw/cun/index.html]