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 * $a^n \pm 1$ 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 localhost)