Differences between revisions 3 and 5 (spanning 2 versions)
⇤ ← Revision 3 as of 2007-01-23 02:01:03 →
Size: 1523
Editor: TimothyClemans
Comment:
← Revision 5 as of 2007-01-23 02:41:17 → ⇥
Size: 1759
Editor: TimothyClemans
Comment:
Deletions are marked like this. Additions are marked like this.
Line 7: Line 7:
 3n + 1 L, M for . . . . 66
 5n − 1 n odd L, M for n = 10k − 5 ≤ 745 . . . .		  * $3^n + 1$ L, M for . . . . 66
 * $5^n − 1$ where n is odd L, M for n = 10k − 5 ≤ 745 . . . .
Line 11: Line 11:
 5n + 1 .................. 94
 6n − 1 n odd n < 330 . . . . . . . . . . . . . . . . . . 102		  * $5^n + 1$ .................. 94
 * $6^n − 1$ where n is odd n < 330 . . . . . . . . . . . . . . . . . . 102
Line 14: Line 14:
 6n + 1
 7n − 1 n odd n < 300 . . . . . . . . . . . . . . . . . . 116		  * $6^n + 1$
 * $7^n − 1$ where n is odd n < 300 . . . . . . . . . . . . . . . . . . 116
Line 17: Line 17:
 7n + 1
10n − 1 n odd n < 330 ..... ......... . . . . 129		  * $7^n + 1$
 * $10^n − 1$ where n is odd n < 330 ..... ......... . . . . 129
Line 20: Line 20:
10n + 1 L, M for . . . . 133
11n − 1 n odd n < 240 ..... ......... . . . . 142		  * $10^n + 1$ L, M for . . . . 133
 * $11^n − 1$ where n is odd n < 240 ..... ......... . . . . 142
Line 23: Line 23:
11n + 1 L, M for . . . . 145
12n − 1 n odd n < 240 ..... ......... . . . . 152		  * $11^n + 1$ L, M for . . . . 145
 * $12^n − 1$ where n is odd n < 240 ..... ......... . . . . 152
Line 26: Line 26:
12n + 1 L, M for . . . . 155  * $12^n + 1$ L, M for . . . . 155

 * $a^n \pm 1$ for $a ≤ 13$ and $a$ not a perfect number [http://wwwmaths.anu.edu.au/~brent/factors.html]

  • 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

  • a^n \pm 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)