1Math::NumSeq::PythagoreUasneHrypCootnst(r3i)buted Perl DMoactuhm:e:nNtuamtSieoqn::PythagoreanHypots(3)
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NAME

6       Math::NumSeq::PythagoreanHypots -- hypotenuses of Pythagorean triples
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SYNOPSIS

9        use Math::NumSeq::PythagoreanHypots;
10        my $seq = Math::NumSeq::PythagoreanHypots->new;
11        my ($i, $value) = $seq->next;
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DESCRIPTION

14       This is integers occurring as the hypotenuse of a Pythagorean triple,
15       ie. the C in A^2+B^2=C^2.
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17           5, 10, 13, 15, 17, 20, ...
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19       For example 13 is in the sequence because it occurs as 1^2+12^2 = 13^2.
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21       It can be shown that this is all integers which have at least one prime
22       factor of the form 4k+1.
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24   Primitive Triples
25       Option "pythagorean_type => "primitive"" restricts to those hypotenuses
26       occurring in primitive triples.  For any triple A,B,C a multiple
27       k*A,k*B,k*C is also a triple.  The primitive triples are those where
28       A,B have no common factor which could be divided out.
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30           5, 13, 17, 25, 29, 37, ...
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32       It can be shown these are integers comprised only of prime factors
33       4k+1.  (For all triples at least one 4k+1 prime factor, and for
34       primitive triples all 4k+1 prime factors.)
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FUNCTIONS

37       See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence
38       classes.
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40       "$seq = Math::NumSeq::PythagoreanHypots->new ()"
41       "$seq = Math::NumSeq::PythagoreanHypots->new (pythagorean_type =>
42       $str)"
43           Create and return a new sequence object.
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45       "$bool = $seq->pred($value)"
46           Return true if $value occurs as a hypotenuse in a Pythagorean
47           triple.
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49           This calculation requires checking the prime factors of $value (to
50           look for either one or all 4k+1).  In the current code a hard limit
51           of 2**32 is placed on $value in the interests of not going into a
52           near-infinite loop.
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SEE ALSO

55       Math::NumSeq, Math::NumSeq::Cubes
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57       Math::PlanePath::PythagoreanTree
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HOME PAGE

60       <http://user42.tuxfamily.org/math-numseq/index.html>
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LICENSE

63       Copyright 2010, 2011, 2012, 2013, 2014, 2016, 2019 Kevin Ryde
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65       Math-NumSeq is free software; you can redistribute it and/or modify it
66       under the terms of the GNU General Public License as published by the
67       Free Software Foundation; either version 3, or (at your option) any
68       later version.
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70       Math-NumSeq is distributed in the hope that it will be useful, but
71       WITHOUT ANY WARRANTY; without even the implied warranty of
72       MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
73       General Public License for more details.
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75       You should have received a copy of the GNU General Public License along
76       with Math-NumSeq.  If not, see <http://www.gnu.org/licenses/>.
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80perl v5.32.1                      2021-01-27Math::NumSeq::PythagoreanHypots(3)
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