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MathGroup Archive 2006

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Re: Re: Finding the Number of Pythagorean Triples below a bound

  • To: mathgroup at smc.vnet.net
  • Subject: [mg68428] Re: [mg68409] Re: Finding the Number of Pythagorean Triples below a bound
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Sat, 5 Aug 2006 03:46:05 -0400 (EDT)
  • References: <eaeqa3$53v$1@smc.vnet.net><eakfgm$rl6$1@smc.vnet.net> <200608020923.FAA28520@smc.vnet.net> <79C36C70-E091-4A82-8EC5-0EDC743D081D@mimuw.edu.pl> <easiva$fp3$1@smc.vnet.net> <200608040759.DAA01035@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

On 4 Aug 2006, at 09:59, titus_piezas at yahoo.com wrote:

> Hello Andrzej,
>
> The code I used was this:
>
> c1=Sqrt[N[a^2+b^2-k]];
>
> countTriples[m_]:=Block[{a,b,i=0},For[a=1,a<(10^m/Sqrt[2]),a++,
> For[b=a,b<10^m,b++,If[c1==Round[c1]&&c1<10^m,i++]]];i]
>
> though m=3 takes about 50 sec (in an old comp) while m=4 will  
> prolly be
>
> around 5000 sec (83 mins).
>
>
> -Titus
>


This is very odd indeed. For example, I get:


c1=Sqrt[N[a^2+b^2-k]];


countTriples[m_]:=Block[{a,b,i=0},For[a=1,a<(10^m/Sqrt[2]),a++,
For[b=a,b<10^m,b++,If[c1==Round[c1]&&c1<10^m,i++]]];i]

In[6]:=
k=3;


countTriples[2]

Invalid comparison
     with  0. I attempted.

13

The correct answer is:


f[10^2,-3]


28


Similarly for other values. Your code usually doesn't work on my  
machine and when it does it produces wrong answers.

Andrzej Kozlowski


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