{"id":20747,"date":"2021-09-21T09:00:18","date_gmt":"2021-09-21T03:30:18","guid":{"rendered":"https:\/\/python-programs.com\/?p=20747"},"modified":"2021-11-22T18:36:16","modified_gmt":"2021-11-22T13:06:16","slug":"python-program-for-modular-multiplicative-inverse-from-1-to-n","status":"publish","type":"post","link":"https:\/\/python-programs.com\/python-program-for-modular-multiplicative-inverse-from-1-to-n\/","title":{"rendered":"Python Program for Modular Multiplicative Inverse from 1 to n"},"content":{"rendered":"<p>In the previous article, we have discussed <a href=\"https:\/\/python-programs.com\/python-program-to-find-value-of-y-mod-2-raised-to-power-x\/\">Python Program to Find Value of y Mod (2 raised to power x)<\/a><\/p>\n<p>Given two numbers n and a prime number, the task is to find the modular multiplicative inverse from 1 to the given number n<\/p>\n<p>The modular multiplicative inverse of an is an integer \u2018x&#8217; in such a way that<\/p>\n<p>a x \u2261 1 (mod prime)<\/p>\n<p><strong>Examples:<\/strong><\/p>\n<p><strong>Example1:<\/strong><\/p>\n<p><strong>Input:<\/strong><\/p>\n<pre>Given number = 5\r\nGiven prime number = 7<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<pre id=\"codeOutputPre\">The modular multiplicative inverse from 1 to the given number{ 5 } :\r\n1 4 5 2 3<\/pre>\n<p><strong>Explanation:<\/strong><\/p>\n<pre>For 1, modular inverse is 1 as (1 * 1)%7 is 1\r\nFor 2, modular inverse is 4 as (2 * 4)%7 is 1\r\nFor 3, modular inverse is 6 as (3 * 5)%7 is 1\r\n..\r\n..<\/pre>\n<p><strong>Example2:<\/strong><\/p>\n<p><strong>Input:<\/strong><\/p>\n<pre>Given number = 9\r\nGiven prime number = 11<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<pre id=\"codeOutputPre\">The modular multiplicative inverse from 1 to the given number{ 9 } :\r\n1 6 4 3 9 2 8 7 5<\/pre>\n<h2>Program for Modular Multiplicative Inverse from 1 to n in Python<\/h2>\n<p>Below are the ways to find the modular multiplicative inverse from 1 to the given number n 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 number as static input and store it in a variable.<\/li>\n<li>Give the prime number as static input and store it in another variable.<\/li>\n<li>Create a function to say <strong>modularmultInverse()<\/strong> which takes the iterator value and the given number as the arguments and returns the modular multiplicative inverse from 1 to the given number n.<\/li>\n<li>Inside the function, calculate the iterator value modulus given prime number and store it in the same variable iterator value.<\/li>\n<li>Loop from 1 to the given prime number using the for loop.<\/li>\n<li>Check if the iterator value multiplied by <strong>k<\/strong> (where k is the iterator value of for loop) modulus given prime number is equal to 1 using the if conditional statement.<\/li>\n<li>If it is true, return the value of k.<\/li>\n<li>Return -1.<\/li>\n<li>Loop from 1 to the given number using the for loop.<\/li>\n<li>Pass the iterator value and the given prime number to the\u00a0<strong>modularmultInverse() <\/strong>function and print it.<\/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 modularmultInverse() which takes the iterator value and the\r\n# given number as the arguments and returns the modular multiplicative inverse from 1\r\n# to the given number n.\r\n\r\n\r\ndef modularmultInverse(itrvl, gvn_primenum):\r\n  # Inside the function, calculate the iterator value modulus given prime number and\r\n  # store it in the same variable iterator value.\r\n    itrvl = itrvl % gvn_primenum\r\n    # Loop from 1 to the given prime number using the for loop.\r\n    for k in range(1, gvn_primenum):\r\n     # Check if the iterator value multiplied by k (where k is the iterator value of for loop)\r\n     # modulus given prime number is equal to 1 using the if conditional statement.\r\n        if ((itrvl*k) % gvn_primenum == 1):\r\n          # If it is true, return the value of k.\r\n            return k\r\n    #Return -1.\r\n    return -1\r\n\r\n\r\n# Give the number as static input and store it in a variable.\r\ngvn_numb = 5\r\n# Give the prime number as static input and store it in another variable.\r\ngvn_primenum = 7\r\n# Loop from 1 to the given number using the for loop.\r\nprint(\r\n    \"The modular multiplicative inverse from 1 to the given number{\", gvn_numb, \"} :\")\r\nfor itr in range(1, gvn_numb+1):\r\n  # Pass the iterator value and the given prime number to the\u00a0modularmultInverse() function\r\n  # and print it.\r\n    print(modularmultInverse(itr, gvn_primenum), end=\" \")\r\n<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<pre id=\"codeOutputPre\">The modular multiplicative inverse from 1 to the given number{ 5 } :\r\n1 4 5 2 3<\/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 number as user input using the int(input()) function and store it in a variable.<\/li>\n<li>Give the prime number as user input using the int(input()) function and store it in another variable.<\/li>\n<li>Create a function to say <strong>modularmultInverse()<\/strong> which takes the iterator value and the given number as the arguments and returns the modular multiplicative inverse from 1 to the given number n.<\/li>\n<li>Inside the function, calculate the iterator value modulus given prime number and store it in the same variable iterator value.<\/li>\n<li>Loop from 1 to the given prime number using the for loop.<\/li>\n<li>Check if the iterator value multiplied by <strong>k<\/strong> (where k is the iterator value of for loop) modulus given prime number is equal to 1 using the if conditional statement.<\/li>\n<li>If it is true, return the value of k.<\/li>\n<li>Return -1.<\/li>\n<li>Loop from 1 to the given number using the for loop.<\/li>\n<li>Pass the iterator value and the given prime number to the\u00a0<strong>modularmultInverse() <\/strong>function and print it.<\/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 modularmultInverse() which takes the iterator value and the\r\n# given number as the arguments and returns the modular multiplicative inverse from 1\r\n# to the given number n.\r\n\r\n\r\ndef modularmultInverse(itrvl, gvn_primenum):\r\n  # Inside the function, calculate the iterator value modulus given prime number and\r\n  # store it in the same variable iterator value.\r\n    itrvl = itrvl % gvn_primenum\r\n    # Loop from 1 to the given prime number using the for loop.\r\n    for k in range(1, gvn_primenum):\r\n     # Check if the iterator value multiplied by k (where k is the iterator value of for loop)\r\n     # modulus given prime number is equal to 1 using the if conditional statement.\r\n        if ((itrvl*k) % gvn_primenum == 1):\r\n          # If it is true, return the value of k.\r\n            return k\r\n    #Return -1.\r\n    return -1\r\n    \r\n    \r\n# Give the number as user input using the int(input()) function and store it in a variable.\r\ngvn_numb = int(input(\"Enter some random number = \"))\r\n# Give the prime number as user input using the int(input()) function and \r\n# store it in another variable.\r\ngvn_primenum = int(input(\"Enter some random number = \"))\r\n# Loop from 1 to the given number using the for loop.\r\nprint(\r\n    \"The modular multiplicative inverse from 1 to the given number{\", gvn_numb, \"} :\")\r\nfor itr in range(1, gvn_numb+1):\r\n  # Pass the iterator value and the given prime number to the\u00a0modularmultInverse() function\r\n  # and print it.\r\n    print(modularmultInverse(itr, gvn_primenum), end=\" \")\r\n<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<pre>Enter some random number = 9\r\nEnter some random number = 11\r\nThe modular multiplicative inverse from 1 to the given number{ 9 } :\r\n1 6 4 3 9 2 8 7 5<\/pre>\n<p>If you are learning Python then the <a href=\"https:\/\/python-programs.com\/python-programming-examples-with-output\/\">Python Programming Example<\/a> is for you and gives you a thorough description of concepts for beginners, experienced programmers.<\/p>\n<ul>\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<li><a 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a prime number, the task is to find the modular multiplicative inverse from 1 to the given number n The modular multiplicative inverse of an is an integer \u2018x&#8217; in &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/python-programs.com\/python-program-for-modular-multiplicative-inverse-from-1-to-n\/\"> <span class=\"screen-reader-text\">Python Program for Modular Multiplicative Inverse from 1 to n<\/span> Read More &raquo;<\/a><\/p>\n","protected":false},"author":7,"featured_media":20815,"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 from 1 to n - Python Programs<\/title>\n<meta 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