{"id":20750,"date":"2021-09-30T11:30:20","date_gmt":"2021-09-30T06:00:20","guid":{"rendered":"https:\/\/python-programs.com\/?p=20750"},"modified":"2021-11-22T18:35:29","modified_gmt":"2021-11-22T13:05:29","slug":"python-program-for-given-two-numbers-a-and-b-find-all-x-such-that-a-x-b","status":"publish","type":"post","link":"https:\/\/python-programs.com\/python-program-for-given-two-numbers-a-and-b-find-all-x-such-that-a-x-b\/","title":{"rendered":"Python Program for Given Two Numbers a and b Find all x Such that a % x = b"},"content":{"rendered":"<p>In the previous article, we have discussed <a href=\"https:\/\/python-programs.com\/python-program-for-modular-multiplicative-inverse-from-1-to-n\/\">Python Program for Modular Multiplicative Inverse from 1 to n<\/a><\/p>\n<p>Given two numbers a, b and the task is to find all x such that given a % x = b<\/p>\n<p><strong>Examples:<\/strong><\/p>\n<p><strong>Example1:<\/strong><\/p>\n<p><strong>Input:<\/strong><\/p>\n<pre>Given a value = 21\r\nGiven b value = 5<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<pre id=\"codeOutputPre\">The value of x such that given a%x==b {a,b = 21 5 } =  2<\/pre>\n<p><strong>Explanation:<\/strong><\/p>\n<pre>Here the values of x which satisfy a%x=b are 8,16 because 21%8=5 ,21%16=5.\r\nso total number of possible x are 8,16 i.e 2 values<\/pre>\n<p><strong>Example2:<\/strong><\/p>\n<p><strong>Input:<\/strong><\/p>\n<pre>Given a value = 35\r\nGiven b value = 8<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<pre id=\"codeOutputPre\">The value of x such that given a%x==b {a,b = 35 8 } =  2<\/pre>\n<h2>Program for Given two Numbers a and b Find all x Such that a % x = b in Python<\/h2>\n<p>Below are the ways to find all x such that given a % x = b 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>Import the math module using the import keyword.<\/li>\n<li>Give the number as static input and store it in a variable.<\/li>\n<li>Give the other number as static input and store it in another variable.<\/li>\n<li>Pass the given number two numbers as the arguments to the <strong>a_mod_xisb<\/strong> function.<\/li>\n<li>Create a function to say <strong>a_mod_xisb <\/strong>which takes the given two numbers as the arguments and returns all the values of x such that given a % x = b.<\/li>\n<li>Check if the given number a is less than the given b value using the if conditional statement.<\/li>\n<li>If it is true then print &#8220;There are no solutions possible&#8221;.<\/li>\n<li>Return.<\/li>\n<li>Check if the given <strong>a<\/strong> value is equal to the given <strong>b<\/strong> value using the if conditional statement.<\/li>\n<li>If it is true then print &#8220;Infinite Solutions are possible for the equation&#8221;.<\/li>\n<li>Return.<\/li>\n<li>Take a variable say <strong>cnt<\/strong> and initialize its value to 0.<\/li>\n<li>Subtract the given b value from the given a value and store it in another variable say <strong>rslt<\/strong>.<\/li>\n<li>Calculate the value of square root of (gvn_a_val &#8211; gvn_b_val) using the math.sqrt() function and convert result to an integer using the int() function.<\/li>\n<li>Store it in another variable say <strong>k<\/strong>.<\/li>\n<li>Loop from 1 to the above result <strong>k<\/strong> using the for loop.<\/li>\n<li>Inside the loop, check if the above value of <strong>rslt <\/strong>modulus iterator value is equal to 0 using the if conditional statement.<\/li>\n<li>Again check if the <strong>rslt <\/strong>divided by the iterator value greater than the given b value using the if conditional statement.<\/li>\n<li>If it is true, increment the count value by 1 and store it in the same variable.<\/li>\n<li>Check if the iterator value is greater than the\u00a0given b value using the if conditional statement.<\/li>\n<li>If it is true, increment the count value by 1 and store it in the same variable.<\/li>\n<li>Check if the k multiplied with itself is equal to the <strong>rslt <\/strong>and k greater than the given b value\u00a0using the if conditional statement.<\/li>\n<li>If it is true, decrement the count value by 1 and store it in the same variable.<\/li>\n<li>Print the value of x such that given a%x==b.<\/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\"># Import the math module using the import keyword.\r\nimport math\r\n\r\n# Create a function to say a_mod_xisb which takes the given two numbers as the arguments\r\n# and returns all the values of x such that given a % x = b.\r\n\r\n\r\ndef a_mod_xisb(gvn_a_val, gvn_b_val):\r\n    # Check if the given number a is less than the given b value using the if conditional\r\n    # statement.\r\n\r\n    if (gvn_a_val &lt; gvn_b_val):\r\n      # If it is true then print \"There are no solutions possible\".\r\n        print(\"There are no solutions possible\")\r\n        # Return.\r\n        return\r\n    # Check if the given a value is equal to the given b value using the if conditional\r\n    # statement.\r\n    if (gvn_a_val == gvn_b_val):\r\n        # If it is true then print \"Infinite Solutions are possible for the equation\".\r\n        # Return.\r\n        print(\"Infinite Solutions are possible for the equation\")\r\n        return\r\n    # Take a variable say cnt and initialize its value to 0.\r\n    cnt = 0\r\n    # Subtract the given b value from the given a value and store it in another variable\r\n    # say rslt.\r\n\r\n    rslt = gvn_a_val - gvn_b_val\r\n    # Calculate the value of square root of (gvn_a_val - gvn_b_val) using the math.sqrt()\r\n    # function and convert result to an integer using the int() function.\r\n    # Store it in another variable say k.\r\n    k = (int)(math.sqrt(gvn_a_val - gvn_b_val))\r\n    # Loop from 1 to the above result k using the for loop.\r\n    for itr in range(1, k+1):\r\n      # Inside the loop, check if the above value of rslt modulus iterator value is equal\r\n      # to 0 using the if conditional statement.\r\n        if (rslt % itr == 0):\r\n          # Again check if the rslt divided by the iterator value greater than the given b value\r\n          # using the if conditional statement.\r\n            if (rslt \/ itr &gt; gvn_b_val):\r\n              # If it is true, increment the count value by 1 and store it in the same variable.\r\n                cnt = cnt + 1\r\n      # Check if the iterator value is greater than the\u00a0given b value using the if\r\n          # conditional statement.\r\n            if (itr &gt; gvn_b_val):\r\n                # If it is true, increment the count value by 1 and store it in the same variable.\r\n                cnt = cnt + 1\r\n        # Check if the k multiplied with itself is equal to the rslt and k greater than the\r\n        # given b value\u00a0using the if conditional statement.\r\n    if (k * k == rslt and k &gt; gvn_b_val):\r\n        # If it is true, decrement the count value by 1 and store it in the same variable.\r\n        cnt = cnt - 1\r\n    # Print the value of x such that given a%x==b.\r\n    print(\r\n        \"The value of x such that given a%x==b {a,b =\", gvn_a_val, gvn_b_val, \"} = \", cnt)\r\n\r\n\r\n# Give the number as static input and store it in a variable.\r\ngvn_a_val = 15\r\n# Give the other number as static input and store it in another variable.\r\ngvn_b_val = 2\r\n# Pass the given number two numbers as the arguments to the a_mod_xisb function.\r\na_mod_xisb(gvn_a_val, gvn_b_val)\r\n<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<pre id=\"codeOutputPre\">The value of x such that given a%x==b {a,b = 15 2 } =  1<\/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>Import the math module using the import keyword.<\/li>\n<li>Give the number as user input using the int(input()) function and store it in a variable.<\/li>\n<li>Give the other number as user input using the int(input()) function and store it in another variable.<\/li>\n<li>Pass the given number two numbers as the arguments to the <strong>a_mod_xisb<\/strong> function.<\/li>\n<li>Create a function to say <strong>a_mod_xisb <\/strong>which takes the given two numbers as the arguments and returns all the values of x such that given a % x = b.<\/li>\n<li>Check if the given number a is less than the given b value using the if conditional statement.<\/li>\n<li>If it is true then print &#8220;There are no solutions possible&#8221;.<\/li>\n<li>Return.<\/li>\n<li>Check if the given <strong>a<\/strong> value is equal to the given <strong>b<\/strong> value using the if conditional statement.<\/li>\n<li>If it is true then print &#8220;Infinite Solutions are possible for the equation&#8221;.<\/li>\n<li>Return.<\/li>\n<li>Take a variable say <strong>cnt<\/strong> and initialize its value to 0.<\/li>\n<li>Subtract the given b value from the given a value and store it in another variable say <strong>rslt<\/strong>.<\/li>\n<li>Calculate the value of square root of (gvn_a_val &#8211; gvn_b_val) using the math.sqrt() function and convert result to an integer using the int() function.<\/li>\n<li>Store it in another variable say <strong>k<\/strong>.<\/li>\n<li>Loop from 1 to the above result <strong>k<\/strong> using the for loop.<\/li>\n<li>Inside the loop, check if the above value of <strong>rslt <\/strong>modulus iterator value is equal to 0 using the if conditional statement.<\/li>\n<li>Again check if the <strong>rslt <\/strong>divided by the iterator value greater than the given b value using the if conditional statement.<\/li>\n<li>If it is true, increment the count value by 1 and store it in the same variable.<\/li>\n<li>Check if the iterator value is greater than the\u00a0given b value using the if conditional statement.<\/li>\n<li>If it is true, increment the count value by 1 and store it in the same variable.<\/li>\n<li>Check if the k multiplied with itself is equal to the <strong>rslt <\/strong>and k greater than the given b value\u00a0using the if conditional statement.<\/li>\n<li>If it is true, decrement the count value by 1 and store it in the same variable.<\/li>\n<li>Print the value of x such that given a%x==b.<\/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\"># Import the math module using the import keyword.\r\nimport math\r\n\r\n# Create a function to say a_mod_xisb which takes the given two numbers as the arguments\r\n# and returns all the values of x such that given a % x = b.\r\n\r\n\r\ndef a_mod_xisb(gvn_a_val, gvn_b_val):\r\n    # Check if the given number a is less than the given b value using the if conditional\r\n    # statement.\r\n\r\n    if (gvn_a_val &lt; gvn_b_val):\r\n      # If it is true then print \"There are no solutions possible\".\r\n        print(\"There are no solutions possible\")\r\n        # Return.\r\n        return\r\n    # Check if the given a value is equal to the given b value using the if conditional\r\n    # statement.\r\n    if (gvn_a_val == gvn_b_val):\r\n        # If it is true then print \"Infinite Solutions are possible for the equation\".\r\n        # Return.\r\n        print(\"Infinite Solutions are possible for the equation\")\r\n        return\r\n    # Take a variable say cnt and initialize its value to 0.\r\n    cnt = 0\r\n    # Subtract the given b value from the given a value and store it in another variable\r\n    # say rslt.\r\n\r\n    rslt = gvn_a_val - gvn_b_val\r\n    # Calculate the value of square root of (gvn_a_val - gvn_b_val) using the math.sqrt()\r\n    # function and convert result to an integer using the int() function.\r\n    # Store it in another variable say k.\r\n    k = (int)(math.sqrt(gvn_a_val - gvn_b_val))\r\n    # Loop from 1 to the above result k using the for loop.\r\n    for itr in range(1, k+1):\r\n      # Inside the loop, check if the above value of rslt modulus iterator value is equal\r\n      # to 0 using the if conditional statement.\r\n        if (rslt % itr == 0):\r\n          # Again check if the rslt divided by the iterator value greater than the given b value\r\n          # using the if conditional statement.\r\n            if (rslt \/ itr &gt; gvn_b_val):\r\n              # If it is true, increment the count value by 1 and store it in the same variable.\r\n                cnt = cnt + 1\r\n      # Check if the iterator value is greater than the\u00a0given b value using the if\r\n          # conditional statement.\r\n            if (itr &gt; gvn_b_val):\r\n                # If it is true, increment the count value by 1 and store it in the same variable.\r\n                cnt = cnt + 1\r\n        # Check if the k multiplied with itself is equal to the rslt and k greater than the\r\n        # given b value\u00a0using the if conditional statement.\r\n    if (k * k == rslt and k &gt; gvn_b_val):\r\n        # If it is true, decrement the count value by 1 and store it in the same variable.\r\n        cnt = cnt - 1\r\n    # Print the value of x such that given a%x==b.\r\n    print(\r\n        \"The value of x such that given a%x==b {a,b =\", gvn_a_val, gvn_b_val, \"} = \", cnt)\r\n\r\n\r\n# Give the number as user input using the int(input()) function and\r\n# store it in a variable.\r\ngvn_a_val = int(input(\"Enter some random number = \"))\r\n# Give the other number as user input using the int(input()) function and\r\n# store it in another variable.\r\ngvn_b_val = int(input(\"Enter some random number = \"))\r\n# Pass the given number two numbers as the arguments to the a_mod_xisb function.\r\na_mod_xisb(gvn_a_val, gvn_b_val)\r\n<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<pre>Enter some random number = 35\r\nEnter some random number = 8\r\nThe value of x such that given a%x==b {a,b = 35 8 } = 2<\/pre>\n<p>Explore more <a href=\"https:\/\/python-programs.com\/python-programming-examples-with-output\/\">Example Python Programs<\/a> with output and explanation and practice them for your interviews, assignments and stand out from the rest of the crowd.<\/p>\n<ul>\n<li><a href=\"https:\/\/python-programs.com\/python-program-for-modular-multiplicative-inverse\/\">Python Program for Modular Multiplicative Inverse<\/a><\/li>\n<li><a href=\"https:\/\/python-programs.com\/python-program-to-find-sum-of-modulo-k-of-first-n-natural-numbers\/\"><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Python Program to Find Sum of Modulo K of First N Natural Numbers&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4737,&quot;3&quot;:{&quot;1&quot;:0},&quot;10&quot;:2,&quot;12&quot;:0,&quot;15&quot;:&quot;Arial&quot;}\">Python Program to Find Sum of Modulo K of First N Natural Numbers<\/span><\/a><\/li>\n<li><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><\/li>\n<li><a href=\"https:\/\/python-programs.com\/python-program-for-modular-multiplicative-inverse-from-1-to-n\/\">Python Program for Modular Multiplicative Inverse from 1 to n<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>In the previous article, we have discussed Python Program for Modular Multiplicative Inverse from 1 to n Given two numbers a, b and the task is to find all x such that given a % x = b Examples: Example1: Input: Given a value = 21 Given b value = 5 Output: The value of &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" 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