pythagorean triples exercise

Terry Reedy tjreedy at
Sat Oct 23 21:28:55 CEST 2010

On 10/23/2010 3:34 AM, Lawrence D'Oliveiro wrote:
> In message<8idui6F213U1 at>, Peter Pearson wrote:
>> Is it important to let "a" range all the way up to b, instead of
>> stopping at b-1? (tongue in cheek)
> Makes no difference. :)

The difference is that before one writes the restricted range, one must 
stop and think of the proof that a==b is not possible for a pythagorean 
triple a,b,c. (If a==b, c==sqrt(2)*a and the irrationality of sqrt(2) 
implies that c is also irrational and therefore not integral). The OP 
asked for how to translate the problem description into two loops, one 
nested inside the other, and I gave the simplest, obviously correct, 
brute-force search answer.

If the problem specification had asked for primitive triples (no common 
factors), an additional filter would be required.

Another respondent referred, I believe, to Euclid's formula
However, it is not well suited to the problem specified.

Terry Jan Reedy

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