-> i have experianced almost the same type of thing... i wrote a program years  
-> to find what i call Pythagorean Triples... they are the A, B, and C in 
-> A^2+B^2=C^2... 3 4 5 being the first set... back then, it took many hours fo 
-> those up to 100 to be found... on today's machines, that run is over in 
-> seconds... i've adjusted the program over the years and run it every once in 
-> while just for fun and it still takes only seconds for it to find the triple 
-> up to the highest it can count in that language... 
 
-> )\/(ark 
  
Just for the hell of it, I wrote the following little thing in QBasic. 
It finds the triples, in order - shortest side, middle side, with the 
hypotenuse being whatever it comes out to be. Similar triangles are NOT 
printed. For example, once the thing has found 3,4,5, it ignores 
6,8,10, 9,12,15, etc.. 
  
The first time I tried it, I DIMmed the arrays to hold the same number 
of values as the maximum length of the shortest side. I tried it with 
that number being 100. Interestingly, the arrays were *exactly* full 
when it finished, so there are exactly 100 non-similar Pythagorean 
triangles in which the shortest side is 100 units or less. 
  
Some nice ones show up, such as 119,120,169. I like these triangles in 
which the two shorter sides are almost equal. Too many Pythagorean 
triangles are very long and skinny! 
  
                         dow 
  
----------------------------------------------------- 
  
DEFLNG A-Z 
L = 150 
P = 0 
CLS 
DIM A(1 TO 2 * L), B(1 TO 2 * L) 
FOR A = 1 TO L 
  AA = A * A 
  B = A + 1 
  DO 
    C# = SQR(AA + B * B) 
    C = C# 
    IF C = C# THEN 
      F = 1 
      FOR Q = 1 TO P 
        IF A / A(Q) = B / B(Q) THEN F = 0: EXIT FOR 
      NEXT 
      IF F THEN 
        PRINT A, B, C 
        P = P + 1 
        A(P) = A 
        B(P) = B 
      END IF 
    END IF 
    B = B + 1 
  LOOP UNTIL C# <= B 
NEXT 
PRINT "Number:"; P 
END 
  
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