solutionFinder.sc

class IntWithPow(val i: Int) {
  def pow(n: Int) = Math.pow(i, n).toInt
}

implicit def intToInt(i: Int) = new IntWithPow(i)

// z = ax + by + c
type LinSolution = (Int, Int, Int)

val testRange = 0 to 5

// given (x, y, z), find a solution
def solveLin(x: Int, y: Int, z: Int): Set[LinSolution] = {
  for {
    a <- testRange
    b <- testRange
    c <- testRange
    if a*x + b*y + c == z
  } yield (a, b, c)
}.toSet

solveLin(1, 1, 2)

// z = a*x^b + c*y^d + e*x^f*y^g + h
type QuadSolution = (Int, Int, Int, Int, Int, Int, Int, Int)

def solveQuad(x: Int, y: Int, z: Int): Set[QuadSolution] = {
  for {
    a <- testRange
    b <- testRange
    c <- testRange
    d <- testRange
    e <- testRange
    f <- testRange
    g <- testRange
    h <- testRange
    if a*x.pow(b) + c*y.pow(d) + e*x.pow(f)*y.pow(g) + h == z
  } yield (a, b, c, d, e, f, g, h)
}.toSet

//2^2 + 3^2 = 13
solveQuad(2, 3, 13)