{"id":20702,"date":"2021-09-21T09:00:06","date_gmt":"2021-09-21T03:30:06","guid":{"rendered":"https:\/\/python-programs.com\/?p=20702"},"modified":"2021-11-22T18:36:16","modified_gmt":"2021-11-22T13:06:16","slug":"python-program-to-find-square-root-under-modulo-k-when-k-is-in-form-of-4i-3","status":"publish","type":"post","link":"https:\/\/python-programs.com\/python-program-to-find-square-root-under-modulo-k-when-k-is-in-form-of-4i-3\/","title":{"rendered":"Python Program to Find Square Root Under Modulo k (When k is in Form of 4*i + 3)"},"content":{"rendered":"<p>In the previous article, we have discussed <a href=\"https:\/\/python-programs.com\/python-program-for-array-list-elements-that-appear-more-than-once\/\">Python Program for Array\/List Elements that Appear More than Once<\/a><\/p>\n<p>Given the number N, prime number k and the task is to find the square root of the given number under modulo k(When k is in form of 4*i + 3). Here <strong>i<\/strong> is an integer.<\/p>\n<p><strong>Examples:<\/strong><\/p>\n<p><strong>Example1:<\/strong><\/p>\n<p><strong>Input:<\/strong><\/p>\n<pre>Given prime number k=5\r\nGiven Number = 4<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<pre id=\"codeOutputPre\">The Square root of the given number{ 4 } under modulo k= 2<\/pre>\n<p><strong>Example2:<\/strong><\/p>\n<p><strong>Input:<\/strong><\/p>\n<pre>Given prime number k=3\r\nGiven Number = 5<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<pre id=\"codeOutputPre\">No, we cannot find the square root for a given number<\/pre>\n<h2>Program to Find Square Root Under Modulo k (When k is in Form of 4*i + 3) in Python<\/h2>\n<p>Below are the ways to find the square root of the given number under modulo k (When k is in form of 4*i + 3) 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 prime number k as static input and store it in a variable.<\/li>\n<li>Give the number as static input and store it in another variable.<\/li>\n<li>Pass the given number and k as the arguments to the <strong>sqrt_undermodk<\/strong> function.<\/li>\n<li>Create a function to say <strong>sqrt_undermodk <\/strong>which takes the given number and k as the arguments and returns the square root of the given number under modulo k (When k is in form of 4*i + 3).<\/li>\n<li>Calculate the value of the given number modulus k and store it in the same variable given number.<\/li>\n<li>Loop from 2 to the given k value using the for loop.<\/li>\n<li>Multiply the iterator value with itself and store it in another variable.<\/li>\n<li>Check if the above result modulus k is equal to the given number using the if conditional statement.<\/li>\n<li>If it is true then print the iterator value.<\/li>\n<li>Return and exit the for loop.<\/li>\n<li>Print &#8220;No, we cannot find the square root for a given number&#8221;.<\/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 sqrt_undermodk which takes the given number and k as\r\n# the arguments and returns the square root of the given number under modulo k\r\n# (When k is in form of 4*i + 3).\r\n\r\n\r\ndef sqrt_undermodk(gvn_numb, k):\r\n    # Calculate the value of the given number modulus k and store it in the same variable\r\n    # given number.\r\n    gvn_numb = gvn_numb % k\r\n    # Loop from 2 to the given k value using the for loop.\r\n    for itror in range(2, k):\r\n      # Multiply the iterator value with itself and store it in another variable.\r\n        mul = (itror * itror)\r\n        # Check if the above result modulus k is equal to the given number using the if\r\n        # conditional statement.\r\n        if (mul % k == gvn_numb):\r\n            # If it is true then print the iterator value.\r\n            print(\r\n                \"The Square root of the given number{\", gvn_numb, \"} under modulo k=\", itror)\r\n            # Return and exit the for loop.\r\n            return\r\n    # Print \"No, we cannot find the square root for a given number\".\r\n    print(\"No, we cannot find the square root for a given number\")\r\n\r\n\r\n# Give the prime number k as static input and store it in a variable.\r\nk = 5\r\n# Give the number as static input and store it in another variable.\r\ngvn_numb = 4\r\n# Pass the given number and k as the arguments to the sqrt_undermodk function.\r\nsqrt_undermodk(gvn_numb, k)\r\n<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<pre id=\"codeOutputPre\">The Square root of the given number{ 4 } under modulo k= 2<\/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 prime number k as user input using the int(input()) function and store it in a variable.<\/li>\n<li>Give the number as user input using the int(input()) function and store it in another variable.<\/li>\n<li>Pass the given number and k as the arguments to the <strong>sqrt_undermodk<\/strong> function.<\/li>\n<li>Create a function to say <strong>sqrt_undermodk <\/strong>which takes the given number and k as the arguments and returns the square root of the given number under modulo k (When k is in form of 4*i + 3).<\/li>\n<li>Calculate the value of the given number modulus k and store it in the same variable given number.<\/li>\n<li>Loop from 2 to the given k value using the for loop.<\/li>\n<li>Multiply the iterator value with itself and store it in another variable.<\/li>\n<li>Check if the above result modulus k is equal to the given number using the if conditional statement.<\/li>\n<li>If it is true then print the iterator value.<\/li>\n<li>Return and exit the for loop.<\/li>\n<li>Print &#8220;No, we cannot find the square root for a given number&#8221;.<\/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 sqrt_undermodk which takes the given number and k as\r\n# the arguments and returns the square root of the given number under modulo k\r\n# (When k is in form of 4*i + 3).\r\n\r\n\r\ndef sqrt_undermodk(gvn_numb, k):\r\n    # Calculate the value of the given number modulus k and store it in the same variable\r\n    # given number.\r\n    gvn_numb = gvn_numb % k\r\n    # Loop from 2 to the given k value using the for loop.\r\n    for itror in range(2, k):\r\n      # Multiply the iterator value with itself and store it in another variable.\r\n        mul = (itror * itror)\r\n        # Check if the above result modulus k is equal to the given number using the if\r\n        # conditional statement.\r\n        if (mul % k == gvn_numb):\r\n            # If it is true then print the iterator value.\r\n            print(\r\n                \"The Square root of the given number{\", gvn_numb, \"} under modulo k=\", itror)\r\n            # Return and exit the for loop.\r\n            return\r\n    # Print \"No, we cannot find the square root for a given number\".\r\n    print(\"No, we cannot find the square root for a given number\")\r\n\r\n\r\n# Give the prime number k as user input using the int(input()) function and \r\n# store it in a variable.\r\nk = int(input(\"Enter some random number = \"))\r\n# Give the number as user input using the int(input()) function and \r\n# store it in another variable.\r\ngvn_numb = int(input(\"Enter some random number = \"))\r\n# Pass the given number and k as the arguments to the sqrt_undermodk function.\r\nsqrt_undermodk(gvn_numb, k)\r\n<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<pre>Enter some random number = 7\r\nEnter some random number = 2\r\nThe Square root of the given number{ 2 } under modulo k= 3<\/pre>\n<p>Find a comprehensive collection of <a href=\"https:\/\/python-programs.com\/python-programming-examples-with-output\/\">Examples of Python Programs<\/a> ranging from simple ones to complex ones to guide you throughout your coding journey.<\/p>\n<ul>\n<li><a href=\"https:\/\/python-programs.com\/python-program-to-calculate-electricity-bill\/\">Python Program to Calculate Electricity Bill<\/a><\/li>\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<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>In the previous article, we have discussed Python Program for Array\/List Elements that Appear More than Once Given the number N, prime number k and the task is to find the square root of the given number under modulo k(When k is in form of 4*i + 3). Here i is an integer. Examples: Example1: &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/python-programs.com\/python-program-to-find-square-root-under-modulo-k-when-k-is-in-form-of-4i-3\/\"> <span class=\"screen-reader-text\">Python Program to Find Square Root Under Modulo k (When k is in Form of 4*i + 3)<\/span> Read More &raquo;<\/a><\/p>\n","protected":false},"author":7,"featured_media":20735,"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 to Find Square Root Under Modulo k (When k is in Form of 4*i + 3) - 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-to-find-square-root-under-modulo-k-when-k-is-in-form-of-4i-3\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Python Program to Find Square Root Under Modulo k (When k is in Form of 4*i + 3) - Python Programs\" \/>\n<meta property=\"og:description\" content=\"In the previous article, we have discussed Python Program for Array\/List Elements that Appear More than Once Given the number N, prime number k and the task is to find the square root of the given number under modulo k(When k is in form of 4*i + 3). 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Here i is an integer. Examples: Example1: &hellip; Python Program to Find Square Root Under Modulo k (When k is in Form of 4*i + 3) Read More &raquo;","og_url":"https:\/\/python-programs.com\/python-program-to-find-square-root-under-modulo-k-when-k-is-in-form-of-4i-3\/","og_site_name":"Python Programs","article_publisher":"https:\/\/www.facebook.com\/btechgeeks","article_published_time":"2021-09-21T03:30:06+00:00","article_modified_time":"2021-11-22T13:06:16+00:00","og_image":[{"width":1280,"height":720,"url":"https:\/\/python-programs.com\/wp-content\/uploads\/2021\/09\/Program-to-Find-Square-Root-Under-Modulo-k-When-k-is-in-Form-of-4i-3.png","type":"image\/png"}],"twitter_card":"summary_large_image","twitter_creator":"@btech_geeks","twitter_site":"@btech_geeks","twitter_misc":{"Written by":"Vikram Chiluka","Est. reading time":"5 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Organization","@id":"https:\/\/python-programs.com\/#organization","name":"BTech Geeks","url":"https:\/\/python-programs.com\/","sameAs":["https:\/\/www.instagram.com\/btechgeeks\/","https:\/\/www.linkedin.com\/in\/btechgeeks","https:\/\/in.pinterest.com\/btechgeek\/","https:\/\/www.youtube.com\/channel\/UC9MlCqdJ3lKqz2p5114SDIg","https:\/\/www.facebook.com\/btechgeeks","https:\/\/twitter.com\/btech_geeks"],"logo":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/python-programs.com\/#\/schema\/logo\/image\/","url":"https:\/\/python-programs.com\/wp-content\/uploads\/2020\/11\/BTechGeeks.png","contentUrl":"https:\/\/python-programs.com\/wp-content\/uploads\/2020\/11\/BTechGeeks.png","width":350,"height":70,"caption":"BTech Geeks"},"image":{"@id":"https:\/\/python-programs.com\/#\/schema\/logo\/image\/"}},{"@type":"WebSite","@id":"https:\/\/python-programs.com\/#website","url":"https:\/\/python-programs.com\/","name":"Python Programs","description":"Python Programs with Examples, How To Guides on Python","publisher":{"@id":"https:\/\/python-programs.com\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/python-programs.com\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/python-programs.com\/python-program-to-find-square-root-under-modulo-k-when-k-is-in-form-of-4i-3\/#primaryimage","url":"https:\/\/python-programs.com\/wp-content\/uploads\/2021\/09\/Program-to-Find-Square-Root-Under-Modulo-k-When-k-is-in-Form-of-4i-3.png","contentUrl":"https:\/\/python-programs.com\/wp-content\/uploads\/2021\/09\/Program-to-Find-Square-Root-Under-Modulo-k-When-k-is-in-Form-of-4i-3.png","width":1280,"height":720,"caption":"Program to Find Square Root Under Modulo k (When k is in Form of 4i + 3)"},{"@type":"WebPage","@id":"https:\/\/python-programs.com\/python-program-to-find-square-root-under-modulo-k-when-k-is-in-form-of-4i-3\/#webpage","url":"https:\/\/python-programs.com\/python-program-to-find-square-root-under-modulo-k-when-k-is-in-form-of-4i-3\/","name":"Python Program to Find Square Root Under Modulo k (When k is in Form of 4*i + 3) - 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