From b4f182024c149c4db917e37850af1923ee6e8a30 Mon Sep 17 00:00:00 2001
From: SowinskiBraeden <braeden@sowinski.dev>
Date: Tue, 8 Sep 2026 14:14:16 -0700
Subject: [PATCH] lab01

---
 labs/01/lab1.ex                     | 36 +++++++++++++++++++++++++++++
 lectures/01/lec1.ex                 |  2 +-
 lectures/01/{notes.exs => notes.ex} |  0
 3 files changed, 37 insertions(+), 1 deletion(-)
 create mode 100644 labs/01/lab1.ex
 rename lectures/01/{notes.exs => notes.ex} (100%)

diff --git a/labs/01/lab1.ex b/labs/01/lab1.ex
new file mode 100644
index 0000000..032e2a5
--- /dev/null
+++ b/labs/01/lab1.ex
@@ -0,0 +1,36 @@
+defmodule Lab1 do
+  # Question 1 - Multiplicitive inverse of a module n
+  defp inverse_mod(r, t, newr, _) when newr == 0 do {r, t} end
+  defp inverse_mod(r, t, newr, newt) do
+    q = div(r, newr)
+    inverse_mod(
+      newr,
+      newt,
+      r - q * newr,
+      t - q * newt
+    )
+  end
+
+  def inverse_mod(a, n) do
+    case inverse_mod(n, 0, a, 1) do
+      {r, _} when r > 1 ->
+        :not_invertable
+
+      {_, t} when t < 0 ->
+        t + n
+
+      {_, t} ->
+        t
+    end
+  end
+
+  # Question 2 - Fast modular exponent
+  defp pow_mod(acc, _, m, _) when m == 0, do: acc
+  defp pow_mod(acc, a, m, n), do: pow_mod(
+    rem(acc * a, n), a, m - 1, n
+  )
+
+  def pow_mod(a, m, n) do
+    rem(pow_mod(1, a, m, n), n)
+  end
+end
diff --git a/lectures/01/lec1.ex b/lectures/01/lec1.ex
index 354afd3..2ead961 100644
--- a/lectures/01/lec1.ex
+++ b/lectures/01/lec1.ex
@@ -11,7 +11,7 @@ defmodule Lec1 do
   def fact2(n) do n * fact2(n - 1) end
 
   def fact3(n) when n <= 0 do 1 end # using guard
-  def fact3(n) do  n * fact3(n - 1) end
+  def fact3(n) do n * fact3(n - 1) end
 
   # What on earth is going on?
   # do: with commas eliminates end?
diff --git a/lectures/01/notes.exs b/lectures/01/notes.ex
similarity index 100%
rename from lectures/01/notes.exs
rename to lectures/01/notes.ex