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Find all Pythagorean triangles with length or height less than or equal to 20

Pythagorean triangles are right angle triangles whose sides comply with the following equation:

a * a + b * b = c * c

where c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides. Find all such triangles where a, b and c are non-zero integers with a and b less than or equal to 20. Sort your results by the size of the hypotenuse. The expected answer is:

[3, 4, 5]
[6, 8, 10]
[5, 12, 13]
[9, 12, 15]
[8, 15, 17]
[12, 16, 20]
[15, 20, 25]
scala
val res = for (
x <- 1 to 20 ;
y <- x to 20 ;
z = Math.sqrt(x*x + y*y) ;
if (z.toInt == z) )
yield (x, y, z.toInt)

res.toList.sortWith { (t1, t2) =>
t1._3 < t2._3
} foreach (println(_))
(for(x <- 1 to 20;
y<- x to 20;
z<- 1 to 30;
if(z*z == x*x + y*y)) yield(x, y, z)
).sortWith(_._3 < _._3) foreach println
( for (
a <- 1 to 20 ;
b <- a to 20 ;
c = math.sqrt( a*a + b*b )
if c.toInt == c
) yield ( a, b, c.toInt )
).sortBy {_._3} foreach println

Greatest Common Divisor

Find the largest positive integer that divides two given numbers without a remainder. For example, the GCD of 8 and 12 is 4.

scala
def gcd(x: Int, y: Int): Int =
if (b == 0) x
else gcd(b, x % y)