3) Pythagorean Triples: A right triangle can have sides that are all integers. A

Question

 3) Pythagorean Triples: A right triangle can have sides that are all 
integers. A set of three integer values for the sides of a right  triangle 
is called a Pythagorean triple. These three sides must satisfy the 
relationship that the sum of the squares of two of the sides is equal to 
the square of the hypotenuse. Find all _unique_ Pythagorean triples for side1, 
side2 and hypotenuse, all no longer than 500. How many are there? 
Note that this problem specifically asks you to exclude the duplicates. 
For example, if you were to check all 
unique Pythagorean Triples less than 5 (rather than 500) your output
must be
3       4       5
That is, it must NOT output both (3,4,5) and (4,3,5). 

Expected sample output:

Number of Pythagorean Triples with duplicates : 772
The Innermost for loop is entered 125000000 times.

Number of Pythagorean Triples (no duplicates) : 386
The Innermost for loop is entered 20708500 times.

Explanation / Answer

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