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"question": {
"questionId": "2301",
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"categoryTitle": "Algorithms",
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"title": "Count Array Pairs Divisible by K",
"titleSlug": "count-array-pairs-divisible-by-k",
"content": "<p>Given a <strong>0-indexed</strong> integer array <code>nums</code> of length <code>n</code> and an integer <code>k</code>, return <em>the <strong>number of pairs</strong></em> <code>(i, j)</code> <em>such that:</em></p>\n\n<ul>\n\t<li><code>0 <= i < j <= n - 1</code> <em>and</em></li>\n\t<li><code>nums[i] * nums[j]</code> <em>is divisible by</em> <code>k</code>.</li>\n</ul>\n\n<p> </p>\n<p><strong>Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [1,2,3,4,5], k = 2\n<strong>Output:</strong> 7\n<strong>Explanation:</strong> \nThe 7 pairs of indices whose corresponding products are divisible by 2 are\n(0, 1), (0, 3), (1, 2), (1, 3), (1, 4), (2, 3), and (3, 4).\nTheir products are 2, 4, 6, 8, 10, 12, and 20 respectively.\nOther pairs such as (0, 2) and (2, 4) have products 3 and 15 respectively, which are not divisible by 2. \n</pre>\n\n<p><strong>Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [1,2,3,4], k = 5\n<strong>Output:</strong> 0\n<strong>Explanation:</strong> There does not exist any pair of indices whose corresponding product is divisible by 5.\n</pre>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 <= nums.length <= 10<sup>5</sup></code></li>\n\t<li><code>1 <= nums[i], k <= 10<sup>5</sup></code></li>\n</ul>\n",
"translatedTitle": "统计可以被 K 整除的下标对数目",
"translatedContent": "<p>给你一个下标从 <strong>0</strong> 开始、长度为 <code>n</code> 的整数数组 <code>nums</code> 和一个整数 <code>k</code> ，返回满足下述条件的下标对 <code>(i, j)</code> 的数目：</p>\n\n<ul>\n\t<li><code>0 <= i < j <= n - 1</code> 且</li>\n\t<li><code>nums[i] * nums[j]</code> 能被 <code>k</code> 整除。</li>\n</ul>\n\n<p> </p>\n\n<p><strong>示例 1：</strong></p>\n\n<pre><strong>输入：</strong>nums = [1,2,3,4,5], k = 2\n<strong>输出：</strong>7\n<strong>解释：</strong>\n共有 7 对下标的对应积可以被 2 整除：\n(0, 1)、(0, 3)、(1, 2)、(1, 3)、(1, 4)、(2, 3) 和 (3, 4)\n它们的积分别是 2、4、6、8、10、12 和 20 。\n其他下标对，例如 (0, 2) 和 (2, 4) 的乘积分别是 3 和 15 ，都无法被 2 整除。 \n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre><strong>输入：</strong>nums = [1,2,3,4], k = 5\n<strong>输出：</strong>0\n<strong>解释：</strong>不存在对应积可以被 5 整除的下标对。\n</pre>\n\n<p> </p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 <= nums.length <= 10<sup>5</sup></code></li>\n\t<li><code>1 <= nums[i], k <= 10<sup>5</sup></code></li>\n</ul>\n",
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"For any element in the array, what is the smallest number it should be multiplied with such that the product is divisible by k?",
"The smallest number which should be multiplied with nums[i] so that the product is divisible by k is k / gcd(k, nums[i]). Now think about how you can store and update the count of such numbers present in the array efficiently."
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