A [[wp:Pythagorean_triple|Pythagorean triple]] is defined as three positive integers <math>(a, b, c)</math> where <math>a < b < c</math>, and <math>a^2+b^2=c^2.</math>

They are called primitive triples if <math>a, b, c</math> are co-prime, that is, if their pairwise greatest common divisors <math>{\rm gcd}(a, b) = {\rm gcd}(a, c) = {\rm gcd}(b, c) = 1</math>. 

Because of their relationship through the Pythagorean theorem, a, b, and c are co-prime if a and b are co-prime (<math>{\rm gcd}(a, b) = 1</math>). &nbsp; 

Each triple forms the length of the sides of a right triangle, whose perimeter is <math>P=a+b+c</math>.


;Task:
The task is to determine how many Pythagorean triples there are with a perimeter no larger than 100 and the number of these that are primitive.


;Extra credit: 
Deal with large values. &nbsp; Can your program handle a maximum perimeter of 1,000,000? &nbsp; What about 10,000,000? &nbsp; 100,000,000?

Note: the extra credit is not for you to demonstrate how fast your language is compared to others; &nbsp; you need a proper algorithm to solve them in a timely manner.


;Related tasks:
* &nbsp; [[Euler's sum of powers conjecture]]  
* &nbsp; [[List comprehensions]]
* &nbsp; [[Pythagorean quadruples]] 
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