{"id":20704,"date":"2021-09-21T09:00:08","date_gmt":"2021-09-21T03:30:08","guid":{"rendered":"https:\/\/python-programs.com\/?p=20704"},"modified":"2021-11-22T18:36:16","modified_gmt":"2021-11-22T13:06:16","slug":"python-program-for-modular-multiplicative-inverse","status":"publish","type":"post","link":"https:\/\/python-programs.com\/python-program-for-modular-multiplicative-inverse\/","title":{"rendered":"Python Program for Modular Multiplicative Inverse"},"content":{"rendered":"<p>In the previous article, we have discussed <a href=\"https:\/\/python-programs.com\/python-program-to-find-square-root-under-modulo-k-when-k-is-in-form-of-4i-3\/\">Python Program to Find Square Root Under Modulo k (When k is in Form of 4*i + 3)<\/a><\/p>\n<p>Given two integers and the task is to find the modular multiplicative inverse of \u2018first number\u2019 under modulo \u2018second number\u2019.<\/p>\n<p>The modular multiplicative inverse is an integer \u2018x\u2019 such that<\/p>\n<p>first number x \u2261 1 (mod second number)<\/p>\n<p>The value of x should be in the range 0 to 1, 2,&#8230;second number-1, i.e. in the integer modulo second number ring.<\/p>\n<p>If and only if the first number and second number are relatively prime (i.e., if gcd( first number, second number) = 1), the multiplicative inverse of &#8220;first number modulo second number&#8221; exists.<\/p>\n<p><strong>Examples:<\/strong><\/p>\n<p><strong>Example1:<\/strong><\/p>\n<p><strong>Input:<\/strong><\/p>\n<pre>Given First Number = 10\r\nGiven Second Number = 17<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<pre id=\"codeOutputPre\">The modular multiplicative inverse of given first number under modulo second number =  12<\/pre>\n<p><strong>Example2:<\/strong><\/p>\n<p><strong>Input:<\/strong><\/p>\n<pre>Given First Number = 4\r\nGiven Second Number = 9<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<pre id=\"codeOutputPre\">The modular multiplicative inverse of given first number under modulo second number =  7<\/pre>\n<h2>Program for Modular Multiplicative Inverse in Python<\/h2>\n<p>Below are the ways to find the modular multiplicative inverse of \u2018first number\u2019 under modulo \u2018second number&#8217; in python.<\/p>\n<ul>\n<li><a href=\"#Using_For_Loop_(Static_Input)\">Using For Loop (Static Input)<\/a><\/li>\n<li><a href=\"#Using_For_loop_(User_Input)\">Using For loop (User Input)<\/a><\/li>\n<\/ul>\n<h3 id=\"Using_For_Loop_(Static_Input)\">Method #1: Using For Loop (Static Input)<\/h3>\n<p><strong>Approach:<\/strong><\/p>\n<ul>\n<li>Give the first number as static input and store it in a variable.<\/li>\n<li>Give the second number as static input and store it in another variable.<\/li>\n<li>Pass the given first and second numbers as the arguments to the <strong>modular_MultInverse<\/strong>\u00a0function.<\/li>\n<li>Create a function to say <strong>modular_MultInverse<\/strong> which takes the given first and second numbers as the arguments and returns the modular multiplicative inverse of \u2018first number\u2019 under modulo \u2018second number\u2019.<\/li>\n<li>Calculate the value of the given first number modulus second number and store it in the same variable first number.<\/li>\n<li>Loop from 1 to the given second number using the for loop.<\/li>\n<li>Multiply the given first number with the iterator value and store it in another variable.<\/li>\n<li>Check if the above result modulus second number is equal to 1 using the if conditional statement.<\/li>\n<li>If it is true, then return the iterator value.<\/li>\n<li>Return 1.<\/li>\n<li>Print the modular multiplicative inverse of \u2018first number\u2019 under modulo \u2018second number&#8217;.<\/li>\n<li>The Exit of the Program.<\/li>\n<\/ul>\n<p><strong>Below is the implementation:<\/strong><\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\"># Create a function to say modular_MultInverse which takes the given first and second\r\n# numbers as the arguments and returns the modular multiplicative inverse of\r\n# \u2018first number\u2019 under modulo \u2018second number\u2019.\r\n\r\n\r\ndef modular_MultInverse(fst_numb, secnd_numb):\r\n  # Calculate the value of the given first number modulus second number and store it in the\r\n  # same variable first number.\r\n    fst_numb = fst_numb % secnd_numb\r\n    # Loop from 1 to the given second number using the for loop.\r\n    for itror in range(1, secnd_numb):\r\n        # Multiply the given first number with the iterator value and store it in\r\n        # another variable.\r\n        mul = (fst_numb * itror)\r\n      # Check if the above result modulus second number is equal to 1 using the if conditional\r\n      # statement.\r\n        if (mul % secnd_numb == 1):\r\n          # If it is true, then return the iterator value.\r\n            return itror\r\n    # Return 1.\r\n    return 1\r\n\r\n\r\n# Give the first number as static input and store it in a variable.\r\nfst_numb = 10\r\n# Give the second number as static input and store it in another variable.\r\nsecnd_numb = 17\r\n# Pass the given first and second numbers as the arguments to the modular_MultInverse\r\n# function.\r\n# Print the modular multiplicative inverse of \u2018first number\u2019 under modulo \u2018second number'.\r\nprint(\"The modular multiplicative inverse of given first number under modulo second number = \",\r\n      modular_MultInverse(fst_numb, secnd_numb))\r\n<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<pre id=\"codeOutputPre\">The modular multiplicative inverse of given first number under modulo second number =  12<\/pre>\n<h3 id=\"Using_For_loop_(User_Input)\">Method #2: Using For loop (User Input)<\/h3>\n<p><strong>Approach:<\/strong><\/p>\n<ul>\n<li>Give the first number as user input using the int(input()) function and store it in a variable.<\/li>\n<li>Give the second number as user input using the int(input()) function and store it in another variable.<\/li>\n<li>Pass the given first and second numbers as the arguments to the <strong>modular_MultInverse<\/strong>\u00a0function.<\/li>\n<li>Create a function to say <strong>modular_MultInverse<\/strong> which takes the given first and second numbers as the arguments and returns the modular multiplicative inverse of \u2018first number\u2019 under modulo \u2018second number\u2019.<\/li>\n<li>Calculate the value of the given first number modulus second number and store it in the same variable first number.<\/li>\n<li>Loop from 1 to the given second number using the for loop.<\/li>\n<li>Multiply the given first number with the iterator value and store it in another variable.<\/li>\n<li>Check if the above result modulus second number is equal to 1 using the if conditional statement.<\/li>\n<li>If it is true, then return the iterator value.<\/li>\n<li>Return 1.<\/li>\n<li>Print the modular multiplicative inverse of \u2018first number\u2019 under modulo \u2018second number&#8217;.<\/li>\n<li>The Exit of the Program.<\/li>\n<\/ul>\n<p><strong>Below is the implementation:<\/strong><\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\"># Create a function to say modular_MultInverse which takes the given first and second\r\n# numbers as the arguments and returns the modular multiplicative inverse of\r\n# \u2018first number\u2019 under modulo \u2018second number\u2019.\r\n\r\n\r\ndef modular_MultInverse(fst_numb, secnd_numb):\r\n  # Calculate the value of the given first number modulus second number and store it in the\r\n  # same variable first number.\r\n    fst_numb = fst_numb % secnd_numb\r\n    # Loop from 1 to the given second number using the for loop.\r\n    for itror in range(1, secnd_numb):\r\n        # Multiply the given first number with the iterator value and store it in\r\n        # another variable.\r\n        mul = (fst_numb * itror)\r\n      # Check if the above result modulus second number is equal to 1 using the if conditional\r\n      # statement.\r\n        if (mul % secnd_numb == 1):\r\n          # If it is true, then return the iterator value.\r\n            return itror\r\n    # Return 1.\r\n    return 1\r\n\r\n\r\n# Give the first number as user input using the int(input()) function and store it in a variable.\r\nfst_numb = int(input(\"Enter some random number = \"))\r\n# Give the second number as user input using the int(input()) function and store it in\r\n# another variable.\r\nsecnd_numb = int(input(\"Enter some random number = \"))\r\n# Pass the given first and second numbers as the arguments to the modular_MultInverse\r\n# function.\r\n# Print the modular multiplicative inverse of \u2018first number\u2019 under modulo \u2018second number'.\r\nprint(\"The modular multiplicative inverse of given first number under modulo second number = \",\r\n      modular_MultInverse(fst_numb, secnd_numb))\r\n<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<pre>Enter some random number = 4\r\nEnter some random number = 9\r\nThe modular multiplicative inverse of given first number under modulo second number = 7<\/pre>\n<p>If you wanna write simple python programs as a part of your coding practice refer to numerous <a href=\"https:\/\/python-programs.com\/python-programming-examples-with-output\/\">Simple Python Program Examples<\/a> existing and learn the approach used.<\/p>\n<ul>\n<li><a href=\"https:\/\/python-programs.com\/python-program-to-check-whether-given-array-or-list-can-form-arithmetic-progression\/\">Python Program to Check Whether given Array or List Can Form Arithmetic Progression<\/a><\/li>\n<li><a href=\"https:\/\/python-programs.com\/python-program-to-calculate-the-surface-area-and-volume-of-a-hemisphere\/\"><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Python Program to Calculate the Surface Area and Volume of a Hemisphere&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4224,&quot;10&quot;:2,&quot;15&quot;:&quot;Arial&quot;}\">Python Program to Calculate the Surface Area and Volume of a Hemisphere<\/span><\/a><\/li>\n<li><a href=\"https:\/\/python-programs.com\/python-program-to-compute-the-perimeter-of-trapezoid\/\"><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Python Program to Compute the Perimeter of Trapezoid&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4224,&quot;10&quot;:2,&quot;15&quot;:&quot;Arial&quot;}\">Python Program to Compute the Perimeter of Trapezoid<\/span><\/a><\/li>\n<li><a href=\"https:\/\/python-programs.com\/python-program-to-find-square-root-under-modulo-k-when-k-is-in-form-of-4i-3\/\">Python Program to Find Square Root Under Modulo k (When k is in Form of 4*i + 3)<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>In the previous article, we have discussed Python Program to Find Square Root Under Modulo k (When k is in Form of 4*i + 3) Given two integers and the task is to find the modular multiplicative inverse of \u2018first number\u2019 under modulo \u2018second number\u2019. The modular multiplicative inverse is an integer \u2018x\u2019 such that &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/python-programs.com\/python-program-for-modular-multiplicative-inverse\/\"> <span class=\"screen-reader-text\">Python Program for Modular Multiplicative Inverse<\/span> Read More &raquo;<\/a><\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":"","jetpack_publicize_message":"","jetpack_is_tweetstorm":false,"jetpack_publicize_feature_enabled":true},"categories":[5],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v18.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Python Program for Modular Multiplicative Inverse - Python Programs<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/python-programs.com\/python-program-for-modular-multiplicative-inverse\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Python Program for Modular Multiplicative Inverse - Python Programs\" \/>\n<meta property=\"og:description\" content=\"In the previous article, we have discussed Python Program to Find Square Root Under Modulo k (When k is in Form of 4*i + 3) Given two integers and the task is to find the modular multiplicative inverse of \u2018first number\u2019 under modulo \u2018second number\u2019. 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