Perl-Sensitive Sunglasses PerlMonks

### Re: pythagorean triples

by chas (Priest)
 on Apr 24, 2006 at 03:16 UTC ( #545188=note: print w/replies, xml ) Need Help??

But that doesn't really give "all" of them - e.g. 9,12,15 isn't of that form, is it? (Of course it is a multiple of 3,4,5 which is of that form...)

Replies are listed 'Best First'.
Re^2: pythagorean triples
by thor (Priest) on Apr 24, 2006 at 03:50 UTC
That's correct, but any integer multiple of a primitive Pythagorean triple is also a Pythagorean triple. (The proof is left as an exercise for the reader) This sequence generates the set of primitive Pythagorean triples (assuming that \$m & \$n are coprime)

thor

The only easy day was yesterday

Well, it's true that the primitive triples are of that form, but not conversely; 6,8,10 occurs for n=3,m=1 (which are coprime), and that triple isn't primitive. So the code generates primitive (i.e. having no common factor) triples, but some others as well. The real point is that it isn't so easy to print a list of all Pythagorean triples without duplication, and I guess that thought was what motivated my reply.
Re^2: pythagorean triples
by jgamble (Pilgrim) on Apr 24, 2006 at 21:21 UTC

True, but it's fairly easy to filter out the non-primitives.

If m and n are both even, skip (a, b, and c will all be divisible by two).

If m and n are both odd, skip (a, b, and c will all be divisible by two).

If m and n have a divisor in common (e.g., GCD{12,3} != 1) skip (a, b, and c will have that factor in common).

The first case can be wrapped up in third case (actually, it can be wrapped up in the second case too), but I find that it makes things clearer to separate them out.

The third case should of course have been written as:

If m and n have a divisor in common (e.g., GCD{m,n} != 1) skip (a, b, and c will have that divisor in common).

Create A New User
Node Status?
node history
Node Type: note [id://545188]
help
Chatterbox?
and all is quiet...

How do I use this? | Other CB clients
Other Users?
Others taking refuge in the Monastery: (4)
As of 2018-05-25 07:05 GMT
Sections?
Information?
Find Nodes?
Leftovers?
Voting Booth?
World peace can best be achieved by:

Results (181 votes). Check out past polls.

Notices?