sum_n_ad_100__modulus_125_fixed.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);
my @array = ();

foreach my $m ($from .. $to) {
  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 if $StopFirstFind;
    }
  }
}