diophantine.rb

require 'benchmark'

def sol_equa(n)
  sol = []

  (n/4.0).floor.downto(0) do |y|
    begin
      x = Math.sqrt(n + 4 * y**2)

      sol.push [x.to_i, y.to_i] if x.to_i == x
    rescue => e
      break
    end
  end

  sol
end

p Benchmark.measure { p sol_equa(20000005) }.real