experimental-projects/oeis-research/Amiram Eldar/Chernick-Carmichael number n prime factors/Lucas-Carmichael/modulo.sf

#!/usr/bin/ruby

func U(k, m) {
    k.divisors.first(-1).map {|d|
        d*k*m - 1
    }
}

for k in (1..40) {
    say [k, U(8128, k).map{ _ % 29}]
}

__END__
var list = []
for p in (primes(3,100000)) {
    var t = (1..p -> lazy.map{|k| [k, U(8128, k).map{_ % p}] }.first { _[1].contains(0).not }[0])

    if (t == 2) {
        say p
    }
}

say list.lcm

#say U(496, 10405375365)


__END__

Mod 3:

  m |
----+---------------------------------------
  1 | [0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1]
  2 | [1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0]
  3 | [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]       # for m = 3*1, the factors or not divisible by 3
  4 | [0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1]
  5 | [1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0]
  6 | [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]       # for m = 3*2, the factors or not divisible by 3
  7 | [0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1]
  8 | [1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0]
  9 | [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]       # for m = 3*3, the factors or not divisible by 3

Mod 5:

  m |
----+----------------------------------------
  1 | [2, 0, 1, 3, 2, 0, 1, 0, 1, 3, 2, 0, 1]
  2 | [0, 1, 3, 2, 0, 1, 3, 1, 3, 2, 0, 1, 3]
  3 | [3, 2, 0, 1, 3, 2, 0, 2, 0, 1, 3, 2, 0]
  4 | [1, 3, 2, 0, 1, 3, 2, 3, 2, 0, 1, 3, 2]
  5 | [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]       # for m = 5*1, the factors are not divisible by 5
  6 | [2, 0, 1, 3, 2, 0, 1, 0, 1, 3, 2, 0, 1]
  7 | [0, 1, 3, 2, 0, 1, 3, 1, 3, 2, 0, 1, 3]
  8 | [3, 2, 0, 1, 3, 2, 0, 2, 0, 1, 3, 2, 0]
  9 | [1, 3, 2, 0, 1, 3, 2, 3, 2, 0, 1, 3, 2]
 10 | [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]       # for m = 5*1, the factors are not divisible by 5

  m |
----+-------------------------------------------------------------------------------------------------------------------------
  1 | [ 8127,  16255,  32511,  65023,  130047,  260095,  520191,  1032255,  2064511,  4129023,  8258047,  16516095,  33032191]
  2 | [16255,  32511,  65023, 130047,  260095,  520191, 1040383,  2064511,  4129023,  8258047, 16516095,  33032191,  66064383]
  3 | [24383,  48767,  97535, 195071,  390143,  780287, 1560575,  3096767,  6193535, 12387071, 24774143,  49548287,  99096575]
  4 | [32511,  65023, 130047, 260095,  520191, 1040383, 2080767,  4129023,  8258047, 16516095, 33032191,  66064383, 132128767]
  5 | [40639,  81279, 162559, 325119,  650239, 1300479, 2600959,  5161279, 10322559, 20645119, 41290239,  82580479, 165160959]
  6 | [48767,  97535, 195071, 390143,  780287, 1560575, 3121151,  6193535, 12387071, 24774143, 49548287,  99096575, 198193151]
  7 | [56895, 113791, 227583, 455167,  910335, 1820671, 3641343,  7225791, 14451583, 28903167, 57806335, 115612671, 231225343]
  8 | [65023, 130047, 260095, 520191, 1040383, 2080767, 4161535,  8258047, 16516095, 33032191, 66064383, 132128767, 264257535]
  9 | [73151, 146303, 292607, 585215, 1170431, 2340863, 4681727,  9290303, 18580607, 37161215, 74322431, 148644863, 297289727]
 10 | [81279, 162559, 325119, 650239, 1300479, 2600959, 5201919, 10322559, 20645119, 41290239, 82580479, 165160959, 330321919]