Problem 064: (source):

```
object Euler064 extends EulerApp {
case class Root (root :Int, add :Int, div :Int) {
def expand = {
val term = ((math.sqrt(root) + add)/div).toInt
val nadd = term*div - add
(term, Root(root, nadd, (root - nadd*nadd)/div))
}
override def toString = "(√" + root + "+" + add + ")/" + div
}
def expansion (terms :List[Int], roots :List[Root]) :List[Int] = {
val (term, root) = roots.head.expand
if (root.div == 0 || roots.contains(root)) term :: terms
else expansion(term :: terms, root :: roots)
}
def answer = 1 to 10000 map(n => expansion(Nil, Root(n, 0, 1)::Nil).length) count(_%2==0)
}
```

Here we have a nice little case class to represent a single step in the infinite expansion. The
process of generating the next expansion could be done purely with simple arithmetic, but I'm lazy,
so I just use `math.sqrt`

to obtain the non-fractional part. I don't actually need to keep track of
the terms to obtain the solution, but it was handy to have when I was validating the solution, so I
kept it around. Same goes for `toString`

. I just love that little root sign!