篇名探討完全平方數在數論領域中之研究作者私立高英高級工商.pdfVIP

绡囧悕锛 鎺㈣◣瀹屽叏骞虫柟鏁稿湪鏁歌珫闋樺煙涓箣鐮旂┒ 浣滆€咃細 绉佺珛楂樿嫳楂樼礆宸ュ晢鑱锋キ瀛告牎銆傞儹鑰€鍏冭€佸斧 澹光棌鍓嶈█ 瀹屽叏骞虫柟鏁告槸鏁歌珫涓殑涓€鐠帮紝钘夌敱瀹屽叏骞虫柟鏁镐篃鍙互浜嗚В瀹屽叏骞虫柟鏁稿湪鏁存暩鐨勬噳鐢ㄥ強瀹 缇╋紝鏇村彲琛嶇敓鏇村鏁稿鐩搁棞鍟忛鍙婃噳鐢ㄣ€ 璨斥棌姝ｆ枃 涓€銆佸畾缇╋細 鏁稿涓婏紝骞虫柟鏁革紝鎴栫ū瀹屽叏骞虫柟鏁革紝鏄寚鍙互瀵垚鏌愬€嬫暣鏁哥殑骞虫柟鐨勬暩锛屽嵆鍏跺钩鏂规牴鐐烘暣 鏁哥殑鏁搞€備緥濡傦紝9 = 3 脳 3 锛屽畠鏄竴鍊嬪钩鏂规暩銆傚钩鏂规暩涔熺ū姝ｆ柟褰㈡暩锛岃嫢 n 鐐哄钩鏂规暩锛屽皣 n 鍊 榛炴帓鎴愮煩褰紝鍙互鎺掓垚涓€鍊嬫鏂瑰舰 銆 鑻ュ皣骞虫柟鏁告蹇垫摯灞曞埌鏈夌悊鏁革紝鍓囧叐鍊嬪钩鏂规暩鐨勬瘮浠嶇劧鏄钩鏂规暩锛屼緥濡傦紝 (2 脳 2) / (3 脳 3) = 4/9 = 2/3 脳 2/3 銆 浜屻€佽垑渚 涓夈€侀€氶爡鍏紡 灏嶆柤涓€鍊嬫暣鏁 n 锛屽畠鐨勫钩鏂瑰鎴 2 銆 2绛夋柤闋 n 鍊嬫濂囨暩鐨勫拰 肀 肀 饊倧砜 = 鈭戰€倧 (砜愷€倢 鈭 砜? 銆傚緸1 闁嬪锛岀 n 鍊嬪钩鏂规暩琛ㄧず鐐哄墠涓€鍊嬪钩鏂规暩鍔犱笂绗 n 鍊嬫濂囨暩锛屽 饊倢=砜 52 = 25 = 1 + 3 + 5 + 7 + 9 = 16 + 9 銆傚嵆绗簲鍊嬪钩鏂规暩25 绛夋柤绗洓鍊嬪钩鏂规暩 16 鍔犱笂绗簲鍊嬫濂 鏁革細9 銆 鍥涖€侀仦姝稿叕寮 姣忓€嬪钩鏂规暩鍙互寰炰箣鍓嶇殑鍏╁€嬪钩鏂规暩瑷堢畻寰楀埌锛岄仦鎺ㄥ叕寮忕偤 肀? = 2(n-1)^2-(n-2)^2+2 銆備緥 濡傦紝2脳52 鈭 42 + 2 = 2脳25 鈭 16 + 2 = 50 鈭 16 + 2 = 36 = 62 銆 浜斻€侀€ｇ簩鏁存暩鐨勫拰 骞虫柟鏁搁倓鍙互琛ㄧず鎴愴睕2 = 1 + 1 + 2 + 2 + ... + n 鈭 1 + n 鈭 1 + n 銆備緥濡傦紝42 = 16 = 1 + 1 + 2 + 2 + 3 + 3 + 4 銆傚彲浠ュ皣鍏惰В閲嬬偤鍦ㄩ倞闀风偤 3 鐨勭煩褰笂娣诲姞瀵害鐐 1 鐨勪竴琛屽拰涓€鍒楋紝鍗冲緱鍒伴倞闀 鐐 4 鐨勭煩褰€傞€欏皪鏂艰▓绠楄純澶х殑鏁哥殑骞虫柟鏁搁潪甯告湁鐢ㄣ€備緥濡傦紝 522 = 502 + 50 + 51 + 51 + 52 = 2500 + 204 = 2704. 鍏€佹€ц唱 飦 涓€鍊嬪钩鏂规暩鏄叐鍊嬬浉閯颁笁瑙掑舰鏁镐箣鍜屻€傚叐鍊嬬浉閯板钩鏂规暩涔嬪拰鐐轰竴鍊嬩腑蹇冩鏂瑰舰鏁搞€傛墍鏈夌殑 濂囨暩骞虫柟鏁稿悓鏅備篃鏄腑蹇冨叓閭婂舰鏁搞€ 飦 鍥涘钩鏂瑰拰瀹氱悊瑾槑鎵€鏈夋鏁存暩鍧囧彲琛ㄧず鐐烘渶澶氬洓鍊嬪钩鏂规暩鐨勫拰銆傜壒鍒ョ殑锛屼笁鍊嬪钩鏂规暩涔嬪拰 涓嶈兘琛ㄧず褰㈠ 4k(8m + 7) 鐨勬暩銆傝嫢涓€鍊嬫鏁存暩鍙互琛ㄧず鍥犳暩涓矑鏈夊舰濡 4k + 3 鐨勭礌鏁哥殑 濂囨鏂癸紝鍓囧畠鍙互琛ㄧず鎴愬叐鍊嬪钩鏂规暩涔嬪拰銆 飦 鍦ㄥ崄閫插埗涓紝骞虫柟鏁稿彧鑳戒互 00 锛? 锛? 锛? 锛? 鎴 25 绲愬熬锛 1. 鑻ヤ竴鍊嬫暩浠 0 绲愬熬锛屽畠鐨勫钩鏂规暩浠 00 绲愬熬锛屼笖鍏朵粬鏁稿瓧涔熸鎴愪竴鍊嬪钩鏂规暩 銆 2. 鑻ヤ竴鍊嬫暩浠 1 鎴 9 绲愬熬锛屽畠鐨勫钩鏂规暩浠 1 绲愬熬锛屼笖鍏朵粬鏁稿瓧妲嬫垚鐨勬暩鑳借 4 鏁 闄ゃ€ 3. 鑻ヤ竴鍊嬫暩浠 2 鎴 8 绲愬熬锛屽畠鐨勫钩鏂规暩浠 4 绲愬熬锛屼笖鍏朵粬鏁稿瓧妲嬫垚涓€鍊嬪伓鏁搞€ 4. 鑻ヤ竴鍊嬫暩浠 3