#!/usr/bin/perl -w

use strict;

use v5.10;

use threads;

use threads::shared;

use Math::BigInt;

use Math::BigFloat qw();

# 1 3, 4, 5

# 2 20, 21, 29

# 3 119, 120, 169

# 4 696, 697, 985

# 5 4_059, 4_060, 5_741

# 6 23_660, 23_661, 33_461

# 7 137_903, 137_904, 195_025

# 8 803_760, 803_761, 1_136_689

# 9 4_684_659, 4_684_660, 6_625_109

#10 27_304_196, 27_304_197, 38_613_965

#11 159_140_519, 159_140_520, 225_058_681

#12 927_538_920, 927_538_921, 1_311_738_121

#13 5_406_093_003, 5_406_093_004, 7_645_370_045

#14 31_509_019_100, 31_509_019_101, 44_560_482_149

#15 183_648_021_599, 183_648_021_600, 259_717_522_849

#16 1_070_379_110_496, 1_070_379_110_497, 1_513_744_654_945

$| = 1;

my $precision = -1;

Math::BigFloat->precision($precision);

my $last_a = 3;

my $last_b = 4;

my $last_c = 5;

my $this_a = 20;

my $this_b = 21;

my $this_c = 29;

sub min {

my ($a, $b) = @_;

$a < $b ? $a : $b;

}

sub max {

my ($a, $b) = @_;

$a > $b ? $a : $b;

}

for (;;) {

my $ratio_a = Math::BigFloat->new($this_a)->bdiv($last_a);

my $ratio_b = Math::BigFloat->new($this_b)->bdiv($last_b);

my $ratio_c = Math::BigFloat->new($this_c)->bdiv($last_c);

my $ratio_min = min($ratio_a, min($ratio_b, $ratio_c));

my $ratio_max = max($ratio_a, max($ratio_b, $ratio_c));

my $start = Math::BigInt->new(

Math::BigFloat->new($this_a)->bmul($ratio_min)->bint()

);

my $end = Math::BigFloat->new($this_b)->bmul($ratio_max)->bint() + 1;

my $found = 0;

SEARCH: for (my $next_a = $start; $next_a < $end; $next_a++) {

my $next_b = $next_a + 1;

my $h2 = Math::BigInt->new($next_a) * $next_a

+ Math::BigInt->new($next_b) * $next_b;

my $next_c = Math::BigInt->new((Math::BigFloat->new($h2)->bsqrt() + .5)->bint());

if ($h2 == $next_c * $next_c) {

$last_a = $this_a;

$last_b = $this_b;

$last_c = $this_c;

$this_a = $next_a;

$this_b = $next_b;

$this_c = $next_c;

say "found triple: $this_a, $this_b, $this_c";

$found = 1;

last SEARCH;

}

}

#exit if $this_a == 5_406_093_003;

unless ($found) {

Math::BigFloat->precision(--$precision);

say "precision is now $precision";

}

}