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***drdebcol*** · 09-19-2009, 05:37 PM

Every triangle with one angle 90 degrees has 3 sides that must satisfy relationship that sum of the squares of 2 sides equals to the square of the hypotenuse. For example (3,4,5) is a Pythagorean triple because
sqr(3)+sqr(4)=sqr(5) or
9+16=25
Your task is to find triples that are not bigger than 20, and you need to calculate repetition inside of this algorithm ! And you need to sort triples from smallest to biggest !
So here is the code in TPW :

Code:

program pythagorean_triples;

uses wincrt;

 type

   tarray=record

   x,y,z:longint;

 end;

var

  i1,i2,i3,br,i:longint;

  a:array[1..200] of tarray;

function check(i1,i2,i3:longint):boolean;

var

  i:longint;

  b:boolean;

begin

  if br = 0 then

  check:=true

  else

  begin

  b:=false;

  for i:=1 to br do

   if b=false then

    begin

     if (i1=a[i].x) and (i2=a[i].y) and (i3=a[i].z) then

     b:=true;

     if (i1=a[i].y) and (i2=a[i].x) and (i3=a[i].z) then

     b:=true;

     if (i1=a[i].x) and (i2=a[i].z) and (i3=a[i].y) then

     b:=true;

     if (i1=a[i].y) and (i2=a[i].z) and (i3=a[i].x) then

     b:=true;

     if (i1=a[i].z) and (i2=a[i].y) and (i3=a[i].x) then

     b:=true;

     if (i1=a[i].z) and (i2=a[i].x) and (i3=a[i].y) then

     b:=true;

    end;

    if b=false then

    check:=true

    else

    check:=false;

  end;

end;

begin

br:=0;

for i1:=1 to 20 do

for i2:=1 to 20 do

for i3:=1 to 20 do

begin

if sqr(i1)+sqr(i2)=sqr(i3) then

if check(i1,i2,i3) then

begin

  br:=br+1;

  a[br].x:=i1;

  a[br].y:=i2;

  a[br].z:=i3;

end;

end;

for i:=1 to br do

begin

writeln(a[i].x,' ',a[i].y,' ',a[i].z);

end;

end.

As you can see there are 6 solutions of triples inside first 20 numbers :
3 4 5
5 12 13
6 8 10
8 15 17
9 12 15
12 16 20

***drdebcol*** · 12-19-2009, 07:09 AM

Since i didn't write mathematical formulation of Pythagorean Triples, i'll do it now.
Pythagorean Triple is a triple from natural number triples which has a condition of satisfying Pythagorean theorem.
More about Natural numbers (set of Natural numbers N) you can find here :
http://en.wikipedia.org/wiki/Natural_number
And about Pythagorean theorem, you can find here :
http://en.wikipedia.org/wiki/Pythagorean_theorem
So mathematical formulation would look like this :

[Image: 26651_pythagoreantriples.jpg]

Where N^3 is a sign for triple in set of Natural numbers.
V is mathematical "or".
So set of triples "S" are all Pythagorean Triples that can be generated in set of Natural numbers.