import math

// a function to check if three numbers are a valid triple
def is_triple(a, b, c)
    if not (a < b) and (b < c)
        return false
    end

    return (a^2 + b^2) = c^2
end

// a function to check if the numbers are coprime
def is_coprime(a, b, c)
    global math
    return (math.gcd(a, b)=1) && (math.gcd(a, c)=1) && (math.gcd(b, c)=1)
end

// the maximum perimeter to check
perimeter  = 100
perimeter2 = int(perimeter / 2) - 1
perimeter3 = int(perimeter / 3) - 1

// loop though and look for pythagorean triples
ts = 0
ps = 0
for a in range(1, perimeter3)
    for b in range(a + 1, perimeter2)
        for c in range(b + 1, perimeter2)
            if (a + b + c) <= perimeter
                if is_triple(a,b,c)
                    ts += 1
                    print a + ", " + b + ", " + c
                    if is_coprime(a,b,c)
                        ps += 1
                        print " primitive"
                    end
                    println
                end
            end
        end
    end
end

print   "Up to a perimeter of " + perimeter + ", there are " + ts
println " triples, of which " + ps + " are primitive."