鏄皯浜庢垨絳変簬n鐨勬暟涓笌n
渚嬪
錛屽洜涓?,3,5,7鍧囧拰8浜掕川銆?
浠庢鎷夊嚱鏁板紩浼稿嚭鏉ュ湪 鐜 鏂歸潰鐨勪簨瀹炲拰 鎷夋牸鏈楁棩瀹氱悊 鏋勬垚浜?/font> 嬈ф媺瀹氱悊 鐨勮瘉鏄庛?
蠁鍑芥暟鐨勫?/font>
錛堝敮涓鍜?浜掕川鐨勬暟灝辨槸1鏈韓錛夈?
鑻?i>n鏄?/font> 璐ㄦ暟 p鐨?i>k嬈?/font> 騫?/font> 錛?img class="tex" alt="\varphi(n)=p^a-p^{a-1}=(p-1)p^{k-1}" src="http://www.wikilib.com/images/math/1/6/8/168b9412b2bd2cc9c23651930a41da35.png" />錛屽洜涓洪櫎浜?i>p鐨?/font> 鍊嶆暟 澶栵紝鍏朵粬鏁伴兘璺?i>n浜掕川銆?
嬈ф媺鍑芥暟鏄?/font> 縐у嚱鏁?/font> 鈥斺旇嫢m,n浜掕川錛?img class="tex" alt="\varphi(mn)=\varphi(m)\varphi(n)" src="http://www.wikilib.com/images/math/a/f/8/af816470528ea56da0d6f390c16e462b.png" />銆傝瘉鏄庯細(xì)璁?i>A, B, C鏄窡m, n, mn浜掕川鐨勬暟鐨勯泦錛屾嵁 涓浗鍓╀綑瀹氱悊 錛?img class="tex" alt="A \times B" src="http://www.wikilib.com/images/math/2/7/a/27a7579d0309d06241abeb0bccb4ac99.png" />鍜?i>C鍙緩绔?/font> 涓涓瀵瑰簲 鐨勫叧緋匯傚洜姝?img class="tex" alt="\varphi(n)" src="http://www.wikilib.com/images/math/4/0/b/40ba55cd3c58225334c65204b80c6ca3.png" />鐨勫間嬌鐢?/font> 綆楁湳鍩烘湰瀹氱悊 渚跨煡錛?
- 鑻?img class="tex" alt="n = \prod_{p\mid n} p^{\alpha_p}" src="http://www.wikilib.com/images/math/0/5/9/059bc0d55499e3a97128e7d8215f52f5.png" />錛?
- 鍒?img class="tex" alt="\varphi(n) = \prod_{p\mid n} p^{\alpha_p-1}(p-1) = n\prod_{p|n}\left(1-\frac{1}{p}\right)" src="http://www.wikilib.com/images/math/c/6/f/c6f9c184f86794f66e1f962a93869f14.png" />銆?
渚嬪
涓庢鎷夊畾鐞嗐佽垂椹皬瀹氱悊鐨勫叧緋?/font>
瀵逛換浣曚袱涓簰璐ㄧ殑姝ｆ暣鏁?i>a, m錛?img class="tex" alt="m\ge2" src="http://www.wikilib.com/images/math/0/8/b/08b9e5eccad5ff4a01eb737ac1606e62.png" />錛屾湁
鍗?/font> 嬈ф媺瀹氱悊
褰?i>m鏄川鏁?i>p鏃訛紝姝ゅ紡鍒欎負(fù)錛?
鍗?/font> 璐歸┈灝忓畾鐞?/font> 銆?