{"id":59457,"date":"2026-03-23T17:49:59","date_gmt":"2026-03-23T09:49:59","guid":{"rendered":"https:\/\/www.wukongsch.com\/blog\/?p=59457"},"modified":"2026-04-29T16:35:04","modified_gmt":"2026-04-29T08:35:04","slug":"amc-congruence-math","status":"publish","type":"post","link":"https:\/\/www.wukongsch.com\/blog\/zh\/amc-congruence-math-post-59457\/","title":{"rendered":"AMC8 \u5907\u8003\u6307\u5357 | \u6570\u8bba\u6c42\u4f59\u6570\/\u4e2a\u4f4d\u6570\u79d2\u6740\u6280\u5de7\uff1a\u540c\u4f59\u95ee\u9898\u8be6\u89e3"},"content":{"rendered":"<div style=\"margin-top: 0px; margin-bottom: 0px;\" class=\"sharethis-inline-share-buttons\" ><\/div>\n<p>\u5728 AMC 8\u8003\u8bd5\u4e2d\uff0c\u60f3\u8981\u51b2\u523a\u5168\u7403\u524d 1%\uff0c<strong>\u6570\u8bba<\/strong>\u5f80\u5f80\u662f\u62c9\u5f00\u5dee\u8ddd\u7684\u5173\u952e\u6a21\u5757\u3002\u5f88\u591a\u6d77\u5916\u5b66\u751f\u548c\u5bb6\u957f\u53d1\u73b0\uff0c\u5f53\u8bd5\u5377\u4e0a\u51fa\u73b0\u201c\u6c42\u4e00\u4e2a\u5de8\u5927\u6570\u5b57\u7684\u4e2a\u4f4d\u6570\u201d\u6216\u201c\u590d\u6742\u7684\u4f59\u6570\u8ba1\u7b97\u201d\u65f6\uff0c\u4f20\u7edf\u7684\u786c\u7b97\u65b9\u6cd5\u4e0d\u4ec5\u8017\u65f6\uff0c\u800c\u4e14\u6781\u6613\u51fa\u9519\u3002\u4eca\u5929\uff0c\u6211\u4eec\u5c31\u6765\u653b\u514b AMC 8 \u6570\u8bba\u4e2d\u7684\u62e6\u8def\u864e\u2014\u2014\u540c\u4f59\u95ee\u9898 (Congruence)\u3002<\/p>\n\n\n\n<p>\u5176\u5b9e\uff0c\u540c\u4f59\u5e76\u4e0d\u964c\u751f\u3002\u60f3\u8c61\u4e00\u4e0b\u6211\u4eec\u6bcf\u5929\u90fd\u5728\u7528\u7684\u201c\u65f6\u949f\u6570\u5b66 (Clock Math)\u201d\uff1a\u73b0\u5728\u662f 10 \u70b9\uff0c\u8fc7 5 \u4e2a\u5c0f\u65f6\u662f\u51e0\u70b9\uff1f10 + 5 = 15\uff0c\u4f46\u5728\u949f\u8868\u4e0a\u662f 3 \u70b9\u3002\u8fd9\u5c31\u662f\u5bf9 12 \u53d6\u4f59\u6570\u3002<\/p>\n\n\n\n<p>\u638c\u63e1\u6b63\u786e\u7684\u6570\u5b66\u601d\u7ef4\uff0c\u6bd4\u76f2\u76ee\u5237\u9898\u66f4\u91cd\u8981\u3002\u4f5c\u4e3a\u4e13\u4e3a\u6d77\u5916\u5c11\u513f\u8bbe\u8ba1\u7684\u6570\u5b66\u57f9\u4f18\u5e73\u53f0\uff0c<strong><a href=\"https:\/\/www.wukongsch.com\/zh\/math\/\">\u609f\u7a7a\u6570\u5b66<\/a><\/strong>\u91c7\u7528\u4e2d\u82f1\u53cc\u8bed\u6559\u5b66\uff0c\u5e2e\u52a9\u5b69\u5b50\u4eec\u8de8\u8d8a\u8bed\u8a00\u969c\u788d\uff0c\u7528\u6700\u5de7\u5999\u7684\u7ade\u8d5b\u601d\u7ef4\u79d2\u6740 AMC 8 \u96be\u9898\u3002\u63a5\u4e0b\u6765\uff0c\u8ba9\u6211\u4eec\u8ddf\u7740\u609f\u7a7a\u6570\u5b66\u7684\u601d\u8def\uff0c\u4e00\u8d77\u63a2\u7d22\u540c\u4f59\u7684\u5965\u79d8\uff01<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" width=\"1024\" height=\"690\" src=\"https:\/\/wp-more.wukongedu.net\/blog\/wp-content\/uploads\/2026\/03\/AMC8-\u540c\u4f59\u95ee\u9898-1024x690.png\" alt=\"AMC8\u6570\u5b66\u540c\u4f59\u95ee\u9898\" class=\"wp-image-59466\" srcset=\"https:\/\/wp-more.wukongedu.net\/blog\/wp-content\/uploads\/2026\/03\/AMC8-\u540c\u4f59\u95ee\u9898-1024x690.png 1024w, https:\/\/wp-more.wukongedu.net\/blog\/wp-content\/uploads\/2026\/03\/AMC8-\u540c\u4f59\u95ee\u9898-300x202.png 300w, https:\/\/wp-more.wukongedu.net\/blog\/wp-content\/uploads\/2026\/03\/AMC8-\u540c\u4f59\u95ee\u9898-768x518.png 768w, https:\/\/wp-more.wukongedu.net\/blog\/wp-content\/uploads\/2026\/03\/AMC8-\u540c\u4f59\u95ee\u9898-920x620.png 920w, https:\/\/wp-more.wukongedu.net\/blog\/wp-content\/uploads\/2026\/03\/AMC8-\u540c\u4f59\u95ee\u9898.png 1058w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%e4%b8%80%e3%80%81-amc-8-%e4%b8%ad%e5%90%8c%e4%bd%99%e9%97%ae%e9%a2%98%e7%9f%a5%e8%af%86%e8%af%a6%e8%a7%a3\"><\/span><strong>\u4e00\u3001 AMC 8 \u4e2d\u540c\u4f59\u95ee\u9898\u77e5\u8bc6\u8be6\u89e3<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u4e3a\u4e86\u5e2e\u52a9\u6d77\u5916\u5b66\u751f\u66f4\u597d\u5730\u7406\u89e3\uff0c\u4ee5\u4e0b\u6838\u5fc3\u77e5\u8bc6\u70b9\u91c7\u7528\u4e2d\u82f1\u53cc\u8bed\u5bf9\u7167\uff1a<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>1.\u4ec0\u4e48\u662f\u540c\u4f59\uff1f(What is Congruence?)<\/strong><\/h3>\n\n\n\n<p>\u5982\u679c\u4e24\u4e2a\u6574\u6570 a \u548c b \u9664\u4ee5\u540c\u4e00\u4e2a\u6b63\u6574\u6570 m \u5f97\u5230\u7684\u4f59\u6570\u76f8\u540c\uff0c\u6211\u4eec\u5c31\u8bf4 a \u548c b \u5bf9\u6a21 m \u540c\u4f59\u3002<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>If two integers a and b have the same remainder when divided by a positive integer m, we say that a and b are congruent modulo m.<\/p>\n<\/blockquote>\n\n\n\n<p><strong>\u6570\u5b66\u8868\u8fbe\uff1a<\/strong> a \u2261 b (mod m)<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>2.\u540c\u4f59\u7684\u6838\u5fc3\u6027\u8d28 (Core Properties of Congruence)<\/strong><\/h3>\n\n\n\n<p>\u638c\u63e1\u4ee5\u4e0b\u4e09\u5927\u6027\u8d28\uff0c\u5c31\u80fd\u5728 AMC 8 \u4e2d\u505a\u5230<strong>\u5316\u5927\u4e3a\u5c0f<\/strong>\uff1a<\/p>\n\n\n\n<p><strong>1.\u52a0\u6cd5\u6027\u8d28 (Addition)\uff1a<\/strong> \u82e5 a \u2261 b (mod m) \u4e14 c \u2261 d (mod m)\uff0c\u5219 a + c \u2261 b + d (mod m)\u3002<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>If a is congruent to b mod m, and c is congruent to d mod m, then their sum is congruent mod m.<\/p>\n<\/blockquote>\n\n\n\n<p><strong>2.\u4e58\u6cd5\u6027\u8d28 (Multiplication)\uff1a<\/strong> \u82e5 a \u2261 b (mod m) \u4e14 c \u2261 d (mod m)\uff0c\u5219 a \u00d7 c \u2261 b \u00d7 d (mod m)\u3002<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>The product of congruent numbers is also congruent modulo m.<\/p>\n<\/blockquote>\n\n\n\n<p><strong>3.\u5e42\u8fd0\u7b97\u6027\u8d28 (Exponentiation) \u2014\u2014 AMC8 \u6700\u9ad8\u9891\u8003\u70b9\uff1a<\/strong> \u82e5 a \u2261 b (mod m)\uff0c\u5219\u5bf9\u4e8e\u4efb\u610f\u6b63\u6574\u6570 k\uff0c\u90fd\u6709 a\u1d4f \u2261 b\u1d4f (mod m)\u3002<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>Raising congruent numbers to the same power preserves the congruence modulo m.<\/p>\n<\/blockquote>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>3.AMC8 \u4e2d\u7684\u5e38\u89c1\u8003\u6cd5 (Common Applications in AMC 8)<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u6c42\u5c3e\u6570\/\u4e2a\u4f4d\u6570 (Finding the units digit)\uff1a<\/strong> \u672c\u8d28\u4e0a\u5c31\u662f\u6c42\u8be5\u6570\u5bf9 10 \u53d6\u6a21\u7684\u540c\u4f59\u6570 (equivalent to finding the number modulo 10)\u3002<\/li>\n\n\n\n<li><strong>\u5468\u671f\u95ee\u9898 (Cycle\/Periodic problems)\uff1a<\/strong> \u4f8b\u5982\u65e5\u5386\u3001\u661f\u671f\u51e0\u7684\u63a8\u7b97\uff0c\u672c\u8d28\u662f\u5bf9 7 \u53d6\u6a21 (Calculating days of the week, modulo 7)\u3002<\/li>\n<\/ul>\n\n\n<div class=\"retention-card-new\" data-lang=\"zh\" data-subject=\"MATH\" data-btnName=\"\u7acb\u5373\u514d\u8d39\u8bd5\u542c\" data-subTitle=\"\u9002\u5408\u5168\u74031-12\u5e74\u7ea7\u5b66\u751f\">\r\n    <div class=\"retention-card-l\">\r\n        <div class=\"trustpilot-image\"><\/div>\r\n        <h3><p>\u609f\u7a7a\u56fd\u9645\u6570\u5b66<br \/>\n<span>\u8ba9\u6570\u5b66\u4e4b\u5149\u7167\u4eae\u6bcf\u4e00\u4e2a\u5b69\u5b50\uff01<\/span><\/p>\n<\/h3>\r\n        <p>\u9002\u5408\u5168\u74031-12\u5e74\u7ea7\u5b66\u751f<\/p>\r\n        <a class=\"retention-card-button is-point\" href=\"https:\/\/www.wukongsch.com\/zh\/independent-appointment\/?subject=math&amp;l=c87d1e8c-ec8e-4a2a-83b7-84e0af53d81f&amp;booking_triggerevent=BLOG_DETAIL_MODEL_CTA_BUTTON\" data-buttonname=\"\u7acb\u5373\u9884\u7ea6\u6309\u94ae\u70b9\u51fb\" data-event=\"C_Blog_BLOG_DETAIL_MIDDLE_CTA_BUTTON\" data-expose-buttonname=\"\u7acb\u5373\u9884\u7ea6\u6309\u94ae\u66dd\u5149\" data-expose-event=\"D_Blog_BLOG_DETAIL_MIDDLE_CTA_BUTTON\" target=\"_blank\" title=\"\u7acb\u5373\u514d\u8d39\u8bd5\u542c\">\r\n            \u7acb\u5373\u514d\u8d39\u8bd5\u542c\r\n        <\/a>\r\n    <\/div>\r\n    <div class=\"retention-card-r\"><\/div>\r\n<\/div>\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%e4%ba%8c%e3%80%81-amc-8-%e7%9c%9f%e9%a2%98%e5%ae%9e%e6%88%98%e6%bc%94%e7%bb%83%ef%bc%9a%e5%90%8c%e4%bd%99%e5%ae%9a%e7%90%86%e5%a6%82%e4%bd%95%e5%a4%a7%e6%98%be%e8%ba%ab%e6%89%8b%ef%bc%9f\"><\/span>\u4e8c\u3001 AMC 8 \u771f\u9898\u5b9e\u6218\u6f14\u7ec3\uff1a\u540c\u4f59\u5b9a\u7406\u5982\u4f55\u5927\u663e\u8eab\u624b\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u8ba9\u6211\u4eec\u7528\u4e24\u9053\u7ecf\u5178\u7684 AMC 8 \u771f\u9898\/\u6a21\u62df\u9898\u6765\u7ec3\u7ec3\u624b\uff0c\u770b\u770b\u540c\u4f59\u5b9a\u7406\u5982\u4f55\u5927\u663e\u8eab\u624b\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>\u4f8b\u9898 1\uff1a\u57fa\u7840\u5c3e\u6570\u95ee\u9898 (Example 1: Finding the Last Digit)<\/strong><\/h3>\n\n\n\n<p><strong>Question:<\/strong> What is the units digit of 3\u00b2\u2070\u00b2\u2074?<\/p>\n\n\n\n<p> (3\u76842024\u6b21\u65b9\u7684\u4e2a\u4f4d\u6570\u5b57\u662f\u591a\u5c11\uff1f)<\/p>\n\n\n\n<p><strong>\u89e3\u6790\u6b65\u9aa4\uff1a<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Step 1:<\/strong> \u660e\u786e\u76ee\u6807\u3002\u6c42\u4e2a\u4f4d\u6570\uff0c\u5373\u6c42 3\u00b2\u2070\u00b2\u2074 (mod 10)\u3002<\/li>\n\n\n\n<li><strong>Step 2:<\/strong> \u627e\u89c4\u5f8b\/\u5468\u671f\u3002\u8ba1\u7b97 3 \u7684\u5e42\u6b21\u6a21 10 \u7684\u7ed3\u679c\uff1a 3\u00b9 \u2261 3 3\u00b2 \u2261 9 3\u00b3 \u2261 27 \u2261 7 3\u2074 \u2261 81 \u2261 1 \u6211\u4eec\u53d1\u73b0\uff0c\u5c3e\u6570\u4ee5 3, 9, 7, 1 \u4e3a\u4e00\u4e2a\u5468\u671f\u5faa\u73af\uff0c\u5468\u671f\u957f\u5ea6\u4e3a 4\u3002 <\/li>\n\n\n\n<li><strong>Step 3:<\/strong> \u5229\u7528\u540c\u4f59\u5316\u7b80\u3002\u56e0\u4e3a 2024 \u9664\u4ee5 4 \u7b49\u4e8e 506 \u4f59 0\uff0c\u6240\u4ee5 2024 \u2261 0 (mod 4)\u3002\u8fd9\u610f\u5473\u7740 3\u00b2\u2070\u00b2\u2074 \u7684\u5c3e\u6570\u4e0e 3\u2074 \u7684\u5c3e\u6570\u76f8\u540c\u3002 \u56e0\u6b64 3\u00b2\u2070\u00b2\u2074 \u2261 3\u2074 \u2261 1 (mod 10)\u3002<\/li>\n<\/ul>\n\n\n\n<p><strong>Answer:<\/strong> 1<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>\u4f8b\u9898 2\uff1a\u8fdb\u9636\u4f59\u6570\u8fd0\u7b97<\/strong><\/h3>\n\n\n\n<p><strong>Question:<\/strong> What is the remainder when 2023 \u00d7 2024 \u00d7 2025 is divided by 7? <\/p>\n\n\n\n<p>(\u5f53 2023 \u00d7 2024 \u00d7 2025 \u9664\u4ee5 7 \u65f6\uff0c\u4f59\u6570\u662f\u591a\u5c11\uff1f)<\/p>\n\n\n\n<p><strong>\u89e3\u6790\u6b65\u9aa4\uff1a<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Step 1:<\/strong> \u5343\u4e07\u4e0d\u8981\u76f4\u63a5\u76f8\u4e58\uff01\u6570\u5b57\u592a\u5927\u6781\u6613\u7b97\u9519\u3002\u8fd9\u91cc\u6211\u4eec\u8981\u5229\u7528\u540c\u4f59\u7684\u4e58\u6cd5\u6027\u8d28\u3002 <\/li>\n\n\n\n<li><strong>Step 2:<\/strong> \u5206\u522b\u6c42\u6bcf\u4e2a\u6570\u6a21 7 \u7684\u4f59\u6570\u3002\n<ul class=\"wp-block-list\">\n<li>2023 \/ 7 = 289 \u4f59 0\uff0c\u6240\u4ee5 2023 \u2261 0 (mod 7)<\/li>\n\n\n\n<li>2024 \u6bd4 2023 \u5927 1\uff0c\u6240\u4ee5 2024 \u2261 1 (mod 7)<\/li>\n\n\n\n<li>2025 \u6bd4 2023 \u5927 2\uff0c\u6240\u4ee5 2025 \u2261 2 (mod 7)<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Step 3:<\/strong> \u5c06\u4f59\u6570\u76f8\u4e58\u3002 0 \u00d7 1 \u00d7 2 = 0 \u2261 0 (mod 7)<\/li>\n<\/ul>\n\n\n\n<p><strong>Answer:<\/strong> 0<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%e4%b8%89%e3%80%81-%e5%90%8c%e4%bd%99%e7%9f%a5%e8%af%86%e7%82%b9%e6%80%bb%e7%bb%93%e4%b8%8eamc8%e5%a4%87%e8%80%83%e5%bb%ba%e8%ae%ae\"><\/span><strong>\u4e09\u3001 \u540c\u4f59\u77e5\u8bc6\u70b9\u603b\u7ed3\u4e0eAMC8\u5907\u8003\u5efa\u8bae<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u901a\u8fc7\u4e0a\u9762\u7684\u4f8b\u9898\u53ef\u4ee5\u770b\u51fa\uff0c\u540c\u4f59\u95ee\u9898\u5728\u7b80\u5316\u5927\u6570\u8fd0\u7b97\u3001\u8282\u7701\u8003\u8bd5\u65f6\u95f4\u4e0a\u6709\u7740\u5de8\u5927\u7684\u4f18\u52bf\u3002\u638c\u63e1\u201c\u5316\u5927\u4e3a\u5c0f\u201d\u7684\u6a21\u8fd0\u7b97\u601d\u7ef4\uff0c\u662f\u7a81\u7834 AMC 8 \u8003\u8bd5\u4e2d\u7b2c 15 \u9898\u5230\u7b2c 25 \u9898\u9ad8\u96be\u5ea6\u9898\u76ee\u7684\u91d1\u94a5\u5319\u3002<\/p>\n\n\n\n<p>\u6570\u5b66\u7ade\u8d5b\u62fc\u7684\u4ece\u6765\u4e0d\u4ec5\u662f\u5237\u9898\u91cf\uff0c\u66f4\u662f<strong>\u5e95\u5c42\u903b\u8f91\u548c\u89e3\u9898\u601d\u7ef4<\/strong>\u3002<\/p>\n\n\n\n<p><strong><a href=\"https:\/\/www.wukongsch.com\/zh\/\">\u609f\u7a7a\u6559\u80b2<\/a><\/strong>\u62e5\u6709\u9876\u5c16\u7684\u6559\u7814\u56e2\u961f\uff0c\u4e13\u4e3a\u6d77\u5916\u5b66\u751f\u6253\u9020\u4e86\u7cfb\u7edf\u5316\u7684 AMC 8 \u5907\u8003\u8bfe\u7a0b\u3002\u901a\u8fc7\u4e2d\u82f1\u53cc\u8bed\u6388\u8bfe\uff0c\u6211\u4eec\u4e0d\u4ec5\u80fd\u8ba9\u5b69\u5b50\u65e0\u7f1d\u8854\u63a5\u6d77\u5916\u5168\u82f1\u6587\u7684\u8003\u8bd5\u73af\u5883\uff0c\u8fd8\u80fd\u7528\u6700\u61c2\u534e\u88d4\u5b69\u5b50\u7684\u6559\u5b66\u65b9\u5f0f\uff0c\u5c06\u201c\u540c\u4f59\u201d\u3001\u201c\u6392\u5217\u7ec4\u5408\u201d\u3001\u201c\u51e0\u4f55\u53d8\u6362\u201d\u7b49\u6570\u8bba\u4e0e\u4ee3\u6570\u96be\u70b9\u8bb2\u900f\u3001\u8bb2\u660e\u767d\u3002<\/p>\n\n\n<div class=\"retention-card-new\" data-lang=\"zh\" data-subject=\"MATH\" data-btnName=\"\u7acb\u5373\u514d\u8d39\u8bd5\u542c\" data-subTitle=\"\u9002\u5408\u5168\u74031-12\u5e74\u7ea7\u5b66\u751f\">\r\n    <div class=\"retention-card-l\">\r\n        <div class=\"trustpilot-image\"><\/div>\r\n        <h3><p>\u609f\u7a7a\u56fd\u9645\u6570\u5b66<br \/>\n<span>\u8ba9\u6570\u5b66\u4e4b\u5149\u7167\u4eae\u6bcf\u4e00\u4e2a\u5b69\u5b50\uff01<\/span><\/p>\n<\/h3>\r\n        <p>\u9002\u5408\u5168\u74031-12\u5e74\u7ea7\u5b66\u751f<\/p>\r\n        <a class=\"retention-card-button is-point\" href=\"https:\/\/www.wukongsch.com\/zh\/independent-appointment\/?subject=math&amp;l=c87d1e8c-ec8e-4a2a-83b7-84e0af53d81f&amp;booking_triggerevent=BLOG_DETAIL_MODEL_CTA_BUTTON\" data-buttonname=\"\u7acb\u5373\u9884\u7ea6\u6309\u94ae\u70b9\u51fb\" data-event=\"C_Blog_BLOG_DETAIL_MIDDLE_CTA_BUTTON\" data-expose-buttonname=\"\u7acb\u5373\u9884\u7ea6\u6309\u94ae\u66dd\u5149\" data-expose-event=\"D_Blog_BLOG_DETAIL_MIDDLE_CTA_BUTTON\" target=\"_blank\" title=\"\u7acb\u5373\u514d\u8d39\u8bd5\u542c\">\r\n            \u7acb\u5373\u514d\u8d39\u8bd5\u542c\r\n        <\/a>\r\n    <\/div>\r\n    <div class=\"retention-card-r\"><\/div>\r\n<\/div>","protected":false},"excerpt":{"rendered":"<p>\u5728 AMC 8\u8003\u8bd5\u4e2d\uff0c\u60f3\u8981\u51b2\u523a\u5168\u7403\u524d 1%\uff0c\u6570\u8bba\u5f80\u5f80\u662f\u62c9\u5f00\u5dee\u8ddd\u7684\u5173\u952e\u6a21\u5757\u3002\u5f88\u591a\u6d77\u5916\u5b66\u751f\u548c\u5bb6\u957f\u53d1\u73b0\uff0c\u5f53\u8bd5\u5377\u4e0a\u51fa\u73b0\u201c\u6c42\u4e00\u4e2a\u5de8\u5927\u6570\u5b57\u7684\u4e2a\u4f4d\u6570\u201d\u6216\u201c\u590d\u6742\u7684\u4f59\u6570\u8ba1\u7b97\u201d\u65f6\uff0c\u4f20\u7edf\u7684\u786c\u7b97\u65b9\u6cd5\u4e0d\u4ec5\u8017\u65f6\uff0c\u800c\u4e14\u6781\u6613\u51fa\u9519\u3002\u4eca\u5929\uff0c\u6211\u4eec\u5c31\u6765\u653b\u514b AMC 8 \u6570\u8bba\u4e2d\u7684\u62e6\u8def\u864e\u2014\u2014\u540c\u4f59\u95ee\u9898 (Congruence)\u3002 \u5176\u5b9e\uff0c\u540c\u4f59\u5e76\u4e0d\u964c\u751f\u3002\u60f3\u8c61\u4e00\u4e0b\u6211\u4eec\u6bcf\u5929\u90fd\u5728\u7528\u7684\u201c\u65f6\u949f\u6570\u5b66 (Clock Math)\u201d\uff1a\u73b0\u5728\u662f 10 \u70b9\uff0c\u8fc7 5 \u4e2a\u5c0f\u65f6\u662f\u51e0\u70b9\uff1f10 + 5 = 15\uff0c\u4f46\u5728\u949f\u8868\u4e0a\u662f 3 \u70b9\u3002\u8fd9\u5c31\u662f\u5bf9 12 \u53d6\u4f59\u6570\u3002 \u638c\u63e1\u6b63\u786e\u7684\u6570\u5b66\u601d\u7ef4\uff0c\u6bd4\u76f2\u76ee\u5237\u9898\u66f4\u91cd\u8981\u3002\u4f5c\u4e3a\u4e13\u4e3a\u6d77\u5916\u5c11\u513f\u8bbe\u8ba1\u7684\u6570\u5b66\u57f9\u4f18\u5e73\u53f0\uff0c\u609f\u7a7a\u6570\u5b66\u91c7\u7528\u4e2d\u82f1\u53cc\u8bed\u6559\u5b66\uff0c\u5e2e\u52a9\u5b69\u5b50\u4eec\u8de8\u8d8a\u8bed\u8a00\u969c\u788d\uff0c\u7528\u6700\u5de7\u5999\u7684\u7ade\u8d5b\u601d\u7ef4\u79d2\u6740 AMC 8 \u96be\u9898\u3002\u63a5\u4e0b\u6765\uff0c\u8ba9\u6211\u4eec\u8ddf\u7740\u609f\u7a7a\u6570\u5b66\u7684\u601d\u8def\uff0c\u4e00\u8d77\u63a2\u7d22\u540c\u4f59\u7684\u5965\u79d8\uff01 \u4e00\u3001 AMC 8 \u4e2d\u540c\u4f59\u95ee\u9898\u77e5\u8bc6\u8be6\u89e3 \u4e3a\u4e86\u5e2e\u52a9\u6d77\u5916\u5b66\u751f\u66f4\u597d\u5730\u7406\u89e3\uff0c\u4ee5\u4e0b\u6838\u5fc3\u77e5\u8bc6\u70b9\u91c7\u7528\u4e2d\u82f1\u53cc\u8bed\u5bf9\u7167\uff1a 1.\u4ec0\u4e48\u662f\u540c\u4f59\uff1f(What is Congruence?) \u5982\u679c\u4e24\u4e2a\u6574\u6570 a \u548c b \u9664\u4ee5\u540c\u4e00\u4e2a\u6b63\u6574\u6570 m \u5f97\u5230\u7684\u4f59\u6570\u76f8\u540c\uff0c\u6211\u4eec\u5c31\u8bf4 a \u548c b \u5bf9\u6a21 m \u540c\u4f59\u3002 If two integers a and b have the same remainder when divided by a positive integer m, we say that a and b are congruent modulo m. \u6570\u5b66\u8868\u8fbe\uff1a a \u2261 b (mod m) 2.\u540c\u4f59\u7684\u6838\u5fc3\u6027\u8d28 (Core Properties of Congruence) \u638c\u63e1\u4ee5\u4e0b\u4e09\u5927\u6027\u8d28\uff0c\u5c31\u80fd\u5728 AMC 8 \u4e2d\u505a\u5230\u5316\u5927\u4e3a\u5c0f\uff1a 1.\u52a0\u6cd5\u6027\u8d28 (Addition)\uff1a \u82e5 a \u2261 b (mod m) \u4e14 c \u2261 d (mod m)\uff0c\u5219 a + c \u2261 b + d (mod m)\u3002 If a is congruent to b mod&#46;&#46;&#46;<\/p>\n","protected":false},"author":211806807,"featured_media":59458,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_coblocks_attr":"","_coblocks_dimensions":"","_coblocks_responsive_height":"","_coblocks_accordion_ie_support":"","footnotes":""},"categories":[137471,132672],"tags":[134602,134959],"class_list":["post-59457","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category--zh","category-math-learning-zh","tag-math-learning-zh","tag-overseas-elite-education-zh"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v22.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>AMC8 \u6838\u5fc3\u77e5\u8bc6\u70b9\uff1a\u540c\u4f59\u5b9a\u7406\u4e0e\u540c\u4f59\u95ee\u9898 \uff08\u9644\u4f8b\u9898\u4e2d\u82f1\u8be6\u89e3\uff09<\/title>\n<meta name=\"description\" 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