2016 Update

Task/Modular-inverse/Elixir/modular-inverse.elixir

@@ -0,0 +1,21 @@
+defmodule Modular do
+  def extended_gcd(a, b) do
+    {last_remainder, last_x} = extended_gcd(abs(a), abs(b), 1, 0, 0, 1)
+    {last_remainder, last_x * (if a < 0, do: -1, else: 1)}
+  end
+
+  defp extended_gcd(last_remainder, 0, last_x, _, _, _), do: {last_remainder, last_x}
+  defp extended_gcd(last_remainder, remainder, last_x, x, last_y, y) do
+    quotient   = div(last_remainder, remainder)
+    remainder2 = rem(last_remainder, remainder)
+    extended_gcd(remainder, remainder2, x, last_x - quotient*x, y, last_y - quotient*y)
+  end
+
+  def inverse(e, et) do
+      {g, x} = extended_gcd(e, et)
+      if g != 1, do: raise "The maths are broken!"
+      rem(x+et, et)
+    end
+  end
+
+IO.puts Modular.inverse(42,2017)