def pentagonal?(n)
  ((Math.sqrt((24 * n) + 1) + 1) / 6) % 1 == 0
end

def nth_pentagonal(n)
  n * (3 * n - 1) / 2
end

def pentagonal
  pentagonal_enum = Enumerator.new do |y|
    n = 1
    loop do
      x = n * (3 * n - 1) / 2
      n += 1
      y << x
    end
  end
  pentagonal_enum
end

def sum_and_difference_pentagonal_up_to(n)
  x_list = pentagonal.take_while { |x| x < n }
  y_list = pentagonal.take_while { |y| y < n }

  solutions = []

  x_list.each do |x|
    y_list.each do |y|
      solutions << [x,y] if pentagonal?(x + y) && pentagonal?((x - y).abs)
    end
  end
  solutions
end