sum_n_ad_100__modulus_125.pl

#! /usr/bin/perl
use warnings;

################################################################
#  S = (n+1)^100 + (n+2)^100 + (n+3)^100 + ... + (n+k)^100
#  S mod 125 ? 0 ; n,k egész 1 < k < 156
################################################################
my $StopFirstFind = 1;

my ($from, $to) = (2, 155); # mettol meddig menjen k
my ($x, $sum);
my ($min, $max);

ALL: foreach my $shift (($from - 1) .. ($to - $from)) {
  my @array = ();

  foreach my $n ($from .. $to) {
    my $m = $n + $shift;
    last if $m > $to;

    if (@array) {
      $max = $m if $m > $max;
      $min = $m if $m < $min;
    } else {
      $min = $max = $m;
    }

    # 1 # % 1000 is enough 'cause of %125
    # 2 # perl punctionality is within 16-17 numbers
    #   # 1000 ** 5 == e15, so it must be right
    $x = (($m ** 5 % 1000) ** 5 % 1000) ** 4 % 1000;
    push(@array, $x);
    $sum = 0;
    map {$sum += ($_ % 1000); } @array;
    printf("%3d,%3d  %5d %3d %3d\n", $min, $max, $sum ,$sum % 1000, $sum % 125);
    if (0 == $sum % 125) {
      print "Haha! i got you!\n\n";
      unless (($min % 5 == 0) && ($max == $min)) {
        sleep(4);
        last ALL if $StopFirstFind;
      }
    }
  }
}