added an example of modular exponentiation

ctnt2018/ModularExponentiation.ipynb

@@ -0,0 +1,82 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def mexp(a,x,N):\n",
+    "    m,s=1,a\n",
+    "    while x>0:\n",
+    "        print('{0:5d} {1:5d} {2:10d}'m,s,x)\n",
+    "        if x % 2 ==1:\n",
+    "            m=((m*s) % N)\n",
+    "        s=((s*s) % N)\n",
+    "        x=x//2\n",
+    "    return m"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "1 5 123\n",
+      "5 25 61\n",
+      "125 625 30\n",
+      "125 21028 15\n",
+      "41321 15573 7\n",
+      "23556 62697 3\n",
+      "104119 3316 1\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "55006"
+      ]
+     },
+     "execution_count": 6,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "mexp(5,123,123199)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.6.5"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}

ctnt2018/PminusOneMethod.ipynb

@@ -127,26 +127,6 @@
     "show_factors(640)"
    ]
   },
-  {
-   "cell_type": "code",
-   "execution_count": 38,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "1869036133"
-      ]
-     },
-     "execution_count": 38,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "mexp(5,factorial(10),2**32+1))-1 % (2**32+1)"
-   ]
-  },
   {
    "cell_type": "code",
    "execution_count": null,