欧拉函数据/h1>
已经有账户了?据一种href="//www.parkandroid.com/account/login/?next=/wiki/eulers-totient-function/" class="ax-click" data-ax-id="clicked_signup_modal_login" data-ax-type="link">这里登录。据/一种>据/P.>据/D.一世v>
有关……据/h4>
- 数论据/span>>据/span>
欧拉totient函数据/strong>(也称为Phi函数)计算小于的正整数的数目据span class="katex"> N据/span>它们是互质的据span class="katex"> N据/span>.也就是说,据span class="katex"> ϕ据/span>(据/span>N据/span>)据/span>是据span class="katex"> m据/span>∈据/span>N.据/span>这样据span class="katex"> 1据/span>≤据/span>m据/span>据据/span>N据/span>和据span class="katex"> G据/span>光盘据/span>(据/span>m据/span>那据/span>N据/span>)据/span>=据/span>1据/span>.据/P.>据P.>该函数有关出现在初等数论的许多应用,包括据一种href="//www.parkandroid.com/wiki/eulers-theorem/" class="wiki_link" title="欧拉定理GyD.F4y2Ba" target="_blank">欧拉定理据/一种>那据一种href="//www.parkandroid.com/wiki/primitive-roots-of-unity/" class="wiki_link" title="单位的原始根GyD.F4y2Ba" target="_blank">单位的原始根据/一种>那据一种href="//www.parkandroid.com/wiki/cyclotomic-polynomials/" class="wiki_link" title="圆多项式GyD.F4y2Ba" target="_blank">圆多项式据/一种>, 和据一种href="//www.parkandroid.com/wiki/constructible-numbers/" class="wiki_link" title="可构成的数字GyD.F4y2Ba" target="_blank">可构成的数字据/一种>在几何。据/P.>据P.>据span class="image-caption center">
找据span class="katex"> ϕ据/span>(据/span>1据/span>5.据/span>)据/span>.据/span>
之间的正数小于15时,消除的3或5的倍数,这是据span class="katex"> {据/span>3.据/span>那据/span>5.据/span>那据/span>6.据/span>那据/span>9.据/span>那据/span>1据/span>0.据/span>那据/span>1据/span>2据/span>}据/span>.据/span>剩下的数字是据span class="katex"> {据/span>1据/span>那据/span>2据/span>那据/span>4.据/span>那据/span>7.据/span>那据/span>8.据/span>那据/span>1据/span>1据/span>那据/span>1据/span>3.据/span>那据/span>1据/span>4.据/span>}据/span>那据/span>所以据span class="katex"> ϕ据/span>(据/span>1据/span>5.据/span>)据/span>=据/span>8.据/span>.据/span> □据/span>
计算据span class="katex"> ϕ据/span>(据/span>N据/span>)据/span>
本节的目标是证明了公式据span class="katex"> ϕ据/span>(据/span>N据/span>)据/span>:如果据span class="katex"> P.据/span>1据/span>那据/span>P.据/span>2据/span>那据/span>......据/span>那据/span>P.据/span>K.据/span>是不同的质数除以据span class="katex"> N据/span>那据/span>然后据/P.>据P.>据span class="katex-display"> ϕ据/span>(据/span>N据/span>)据/span>=据/span>N据/span>(据/span>1据/span>-据/span>P.据/span>1据/span>1据/span>)据/span>(据/span>1据/span>-据/span>P.据/span>2据/span>1据/span>)据/span>⋯据/span>(据/span>1据/span>-据/span>P.据/span>K.据/span>1据/span>)据/span>.据/span>
证明始于有关的性能有一定的预赛据span class="katex"> ϕ据/span>.据/span>特别地,定义中的集合据span class="katex"> ϕ据/span>那据/span>由正整数组成据span class="katex"> ≤据/span>N据/span>这是相对素据span class="katex"> N据/span>那据/span>有一个名称;它是表示据/P.>据P.>据span class="katex-display"> (据/span>Z.据/span>/据/span>N据/span>)据/span>*据/span>=据/span>{据/span>m据/span>∈据/span>N.据/span>:据/span>1据/span>≤据/span>m据/span>≤据/span>N据/span>那据/span>G据/span>光盘据/span>(据/span>m据/span>那据/span>N据/span>)据/span>=据/span>1据/span>}据/span>.据/span>
所以据span class="katex"> ϕ据/span>(据/span>N据/span>)据/span>等于大小据span class="katex"> (据/span>Z.据/span>/据/span>N据/span>)据/span>*据/span>.据/span>
省略了关于GCD的要求,就得到了全套据span class="katex">
Z.据/span>/据/span>N据/span>那据/span>已据span class="katex">
N据/span>元素,可以认为是整数据一种href="//www.parkandroid.com/wiki/modular-arithmetic/" class="wiki_link" title="模GyD.F4y2Ba" target="_blank">模据/一种>据span class="katex">
N据/span>.据/span>子集据span class="katex">
(据/span>Z.据/span>/据/span>N据/span>)据/span>*据/span>恰恰是设置据E.m>单位据/E.m>在据span class="katex">
Z.据/span>/据/span>N据/span>.单位是具有乘法逆的元素。这个等价于被互质数据span class="katex">
N据/span>那据/span>经过据一种href="//www.parkandroid.com/wiki/bezouts-identity/" class="wiki_link" title="Bezout的身份GyD.F4y2Ba" target="_blank">Bezout的身份据/一种>.据/P.>据B.lockquote class="theorem">
托能函数为据一种href="//www.parkandroid.com/wiki/multiplicative-function/" class="wiki_link" title="乘法GyD.F4y2Ba" target="_blank">乘法据/一种>:据span class="katex">
ϕ据/span>(据/span>一种据/span>B.据/span>)据/span>=据/span>ϕ据/span>(据/span>一种据/span>)据/span>ϕ据/span>(据/span>B.据/span>)据/span>如果据span class="katex">
肾小球囊性肾病据/span>(据/span>一种据/span>那据/span>B.据/span>)据/span>=据/span>1据/span>.据/span> 左侧数元素据span class="katex">
Z.据/span>∈据/span>(据/span>Z.据/span>/据/span>一种据/span>B.据/span>)据/span>*据/span>右边是有序对据span class="katex">
(据/span>X据/span>那据/span>y据/span>)据/span>那据/span>在哪里据span class="katex">
X据/span>∈据/span>(据/span>Z.据/span>/据/span>一种据/span>)据/span>*据/span>和据span class="katex">
y据/span>∈据/span>(据/span>Z.据/span>/据/span>B.据/span>)据/span>*据/span>.身份将由表现出证明据一种href="//www.parkandroid.com/wiki/bijective-functions/" class="wiki_link" title="双射GyD.F4y2Ba" target="_blank">双射据/一种>据span class="katex">
F据/span>两组之间。据/P.>据P.>这本质上是据一种href="//www.parkandroid.com/wiki/chinese-remainder-theorem/" class="wiki_link" title="中国剩余定理GyD.F4y2Ba" target="_blank">中国剩余定理据/一种>:让据span class="katex">
F据/span>(据/span>Z.据/span>)据/span>是有序对据span class="katex">
(据/span>Z.据/span>国防部据/span>一种据/span>那据/span>Z.据/span>国防部据/span>B.据/span>)据/span>.据/span>这是一个双射,它的逆映射是发送有序对的映射据span class="katex">
(据/span>X据/span>那据/span>y据/span>)据/span>到唯一解mod据span class="katex">
一种据/span>B.据/span>的刻画据/P.>据P.>据span class="katex-display">
Z.据/span>Z.据/span>≡据/span>X据/span>(据/span>m据/span>O.据/span>D.据/span>一种据/span>)据/span>≡据/span>y据/span>(据/span>m据/span>O.据/span>D.据/span>B.据/span>)据/span>.据/span> 请注意,据span class="katex">
Z.据/span>是相对首要的据span class="katex">
一种据/span>B.据/span>当且仅当它是相对素据span class="katex">
一种据/span>和据span class="katex">
B.据/span>.据/span>所以据span class="katex">
F据/span>真的是两者的对立吗据span class="katex">
(据/span>Z.据/span>/据/span>一种据/span>B.据/span>)据/span>*据/span>和据span class="katex">
(据/span>Z.据/span>/据/span>一种据/span>)据/span>*据/span>×据/span>(据/span>Z.据/span>/据/span>B.据/span>)据/span>*据/span>那据/span>如预期的。据span class="katex">
□据/span> 正如任何乘法函数,计算据span class="katex">
ϕ据/span>(据/span>N据/span>)据/span>可以降低到保据span class="katex">
N据/span>作为总理的权力的产物,据span class="katex">
N据/span>=据/span>P.据/span>1据/span>E.据/span>1据/span>......据/span>P.据/span>K.据/span>E.据/span>K.据/span>那据/span>和表达据span class="katex">
ϕ据/span>(据/span>N据/span>)据/span>的乘积据span class="katex">
ϕ据/span>(据/span>P.据/span>一世据/span>E.据/span>一世据/span>)据/span>.据/span> 考虑据span class="katex">
ϕ据/span>(据/span>P.据/span>E.据/span>)据/span>在哪里据span class="katex">
P.据/span>是一个素数。然后该范围内的正整数据span class="katex">
[据/span>1据/span>那据/span>P.据/span>E.据/span>]据/span>这不是互质据span class="katex">
P.据/span>E.据/span>是的数倍据span class="katex">
P.据/span>在这个范围。有据span class="katex">
P.据/span>E.据/span>-据/span>1据/span>这些,所以据/P.>据P.>据span class="katex-display">
ϕ据/span>(据/span>P.据/span>E.据/span>)据/span>=据/span>P.据/span>E.据/span>-据/span>P.据/span>E.据/span>-据/span>1据/span>=据/span>P.据/span>E.据/span>(据/span>1据/span>-据/span>P.据/span>1据/span>)据/span>.据/span> 这导致公式据span class="katex">
ϕ据/span>(据/span>N据/span>)据/span>:据/P.>据B.lockquote class="theorem">
如果据span class="katex">
N据/span>=据/span>P.据/span>1据/span>E.据/span>1据/span>......据/span>P.据/span>K.据/span>E.据/span>K.据/span>那据/span>在哪里据span class="katex">
P.据/span>一世据/span>是素数据span class="katex">
E.据/span>一世据/span>>据/span>0.据/span>那据/span>然后据/P.>据P.>据span class="katex-display">
ϕ据/span>(据/span>N据/span>)据/span>=据/span>N据/span>(据/span>1据/span>-据/span>P.据/span>1据/span>1据/span>)据/span>(据/span>1据/span>-据/span>P.据/span>2据/span>1据/span>)据/span>⋯据/span>(据/span>1据/span>-据/span>P.据/span>K.据/span>1据/span>)据/span>.据/span> 通过可乘,据/P.>据P.>据span class="katex-display">
ϕ据/span>(据/span>N据/span>)据/span>=据/span>ϕ据/span>(据/span>P.据/span>1据/span>E.据/span>1据/span>......据/span>P.据/span>K.据/span>E.据/span>K.据/span>)据/span>=据/span>ϕ据/span>(据/span>P.据/span>1据/span>E.据/span>1据/span>)据/span>......据/span>ϕ据/span>(据/span>P.据/span>K.据/span>E.据/span>K.据/span>)据/span>=据/span>P.据/span>1据/span>E.据/span>1据/span>(据/span>1据/span>-据/span>P.据/span>1据/span>1据/span>)据/span>⋯据/span>P.据/span>K.据/span>E.据/span>K.据/span>(据/span>1据/span>-据/span>P.据/span>K.据/span>1据/span>)据/span>=据/span>(据/span>P.据/span>1据/span>E.据/span>1据/span>......据/span>P.据/span>K.据/span>E.据/span>K.据/span>)据/span>(据/span>1据/span>-据/span>P.据/span>1据/span>1据/span>)据/span>⋯据/span>(据/span>1据/span>-据/span>P.据/span>K.据/span>1据/span>)据/span>=据/span>N据/span>(据/span>1据/span>-据/span>P.据/span>1据/span>1据/span>)据/span>⋯据/span>(据/span>1据/span>-据/span>P.据/span>K.据/span>1据/span>)据/span>.据/span>□据/span> 这个公式也可以由a直接证明据一种href="//www.parkandroid.com/wiki/sieve-of-eratosthenes/" class="wiki_link" title="筛分说法GyD.F4y2Ba" target="_blank">筛分说法据/一种>;如在引言的例子中,除去的倍数据span class="katex">
P.据/span>一世据/span>那据/span>但由于数字可以是多个质数的倍数,正确计算它们需要据一种href="//www.parkandroid.com/wiki/principle-of-inclusion-and-exclusion-problem/" class="wiki_link" title="容斥原理GyD.F4y2Ba" target="_blank">容斥原理据/一种>.据/P.>据B.lockquote class="example">
小于多少个正整数据span class="katex">
9.据/span>0.据/span>0.据/span>是相对素据span class="katex">
9.据/span>0.据/span>0.据/span>还是据/span> 计算据/P.>据P.>据span class="katex-display">
ϕ据/span>(据/span>9.据/span>0.据/span>0.据/span>)据/span>=据/span>9.据/span>0.据/span>0.据/span>(据/span>1据/span>-据/span>2据/span>1据/span>)据/span>(据/span>1据/span>-据/span>3.据/span>1据/span>)据/span>(据/span>1据/span>-据/span>5.据/span>1据/span>)据/span>=据/span>2据/span>4.据/span>0.据/span>.据/span>□据/span>
让据span class="katex">
ϕ据/span>(据/span>N据/span>)据/span>是欧拉函数。如果据span class="katex">
1据/span>≤据/span>N据/span>≤据/span>1据/span>0.据/span>0.据/span>0.据/span>的最小整数值是多少据span class="katex">
N据/span>,最大限度地减少据span class="katex">
N据/span>ϕ据/span>(据/span>N据/span>)据/span>还是据/span> 您可以选择阅读欧拉定理。据/P.>据P.>据span class="katex">
详细信息和假设:据/strong>
属性据/h2>
可乘:据/strong>对于式据span class="katex">
ϕ据/span>(据/span>N据/span>)据/span>可用于证明以下结果,从而推广的可乘据span class="katex">
ϕ据/span>:据/P.>据B.lockquote>
让据span class="katex">
D.据/span>=据/span>G据/span>光盘据/span>(据/span>一种据/span>那据/span>B.据/span>)据/span>.据/span>然后据span class="katex">
ϕ据/span>(据/span>一种据/span>B.据/span>)据/span>=据/span>ϕ据/span>(据/span>一种据/span>)据/span>ϕ据/span>(据/span>B.据/span>)据/span>ϕ据/span>(据/span>D.据/span>)据/span>D.据/span>.据/span> 保理和RSA:据/strong>注意,公式据span class="katex">
ϕ据/span>包括了解的因式分解据span class="katex">
N据/span>.据/span>对于数字据span class="katex">
N据/span>这是两个不同的质数的产品,一种相反的是真实的。也就是说,给定据span class="katex">
N据/span>和据span class="katex">
ϕ据/span>(据/span>N据/span>)据/span>那据/span>和信息据span class="katex">
N据/span>=据/span>P.据/span>问:据/span>对于不同的质数据span class="katex">
P.据/span>和据span class="katex">
问:据/span>那据/span>恢复起来很简单据span class="katex">
P.据/span>和据span class="katex">
问:据/span>.据/span> 要看到这一点,请注意据span class="katex">
ϕ据/span>(据/span>N据/span>)据/span>=据/span>(据/span>P.据/span>-据/span>1据/span>)据/span>(据/span>问:据/span>-据/span>1据/span>)据/span>那据/span>所以据span class="katex">
N据/span>-据/span>ϕ据/span>(据/span>N据/span>)据/span>+据/span>1据/span>=据/span>P.据/span>+据/span>问:据/span>.据/span>会心据span class="katex">
P.据/span>+据/span>问:据/span>和据span class="katex">
P.据/span>问:据/span>就足以找到据span class="katex">
P.据/span>和据span class="katex">
问:据/span>:多项式据span class="katex">
X据/span>2据/span>-据/span>(据/span>N据/span>-据/span>ϕ据/span>(据/span>N据/span>)据/span>+据/span>1据/span>)据/span>X据/span>+据/span>N据/span>因素据span class="katex">
(据/span>X据/span>-据/span>P.据/span>)据/span>(据/span>X据/span>-据/span>问:据/span>)据/span>那据/span>两个根据span class="katex">
P.据/span>那据/span>问:据/span>很容易通过恢复据一种href="//www.parkandroid.com/wiki/quadratic-formula/" class="wiki_link" title="二次方程GyD.F4y2Ba" target="_blank">二次方程据/一种>.据/P.>据P.>这在安全的讨论中很重要据一种href="//www.parkandroid.com/wiki/rsa-encryption/" class="wiki_link" title="RSA加密GyD.F4y2Ba" target="_blank">RSA加密据/一种>;加密方法休止符上的保密的强度据span class="katex">
ϕ据/span>(据/span>N据/span>)据/span>那据/span>上面的段落表明,这等价于因式分解据span class="katex">
N据/span>那据/span>这被广泛认为是一般非常困难的问题。据/P.>据P.>据strong>除数总和:据/strong>这是最著名的性质之一据span class="katex">
ϕ据/span>(据/span>N据/span>)据/span>那据/span>并且它在wiki上讨论据一种href="//www.parkandroid.com/wiki/multiplicative-function/" class="wiki_link" title="乘法功能GyD.F4y2Ba" target="_blank">乘法功能据/一种>:据span class="katex-display">
D.据/span>|据/span>N据/span>Σ据/span>ϕ据/span>(据/span>D.据/span>)据/span>=据/span>N据/span>.据/span>有几种方法来证明这一点,但一个恳求直接的方式进行如下:据/P.>据P.>考虑到分数据span class="katex">
N据/span>1据/span>那据/span>N据/span>2据/span>那据/span>......据/span>那据/span>N据/span>N据/span>.据/span>有明显的据span class="katex">
N据/span>这些。把它们都减到最低项。列表上的新分数都是这种形式的据span class="katex">
D.据/span>一种据/span>那据/span>在哪里据span class="katex">
D.据/span>|据/span>N据/span>和据span class="katex">
一种据/span>是相对首要的据span class="katex">
D.据/span>.据/span>而且它简单地看到,所有这种类型的分数将显示某个地方就行了。据/P.>据P.>这种馏分与分母的数目据span class="katex">
D.据/span>是据span class="katex">
ϕ据/span>(据/span>D.据/span>)据/span>那据/span>所以总数为据span class="katex">
D.据/span>|据/span>N据/span>Σ据/span>ϕ据/span>(据/span>D.据/span>)据/span>.据/span>这表明据span class="katex">
D.据/span>|据/span>N据/span>Σ据/span>ϕ据/span>(据/span>D.据/span>)据/span>=据/span>N据/span>那据/span>如预期的。据/P.>据/D.一世v>
示例应用程序据/h2>
有多少数字据span class="katex"> {据/span>1据/span>那据/span>2据/span>那据/span>......据/span>那据/span>2据/span>0.据/span>0.据/span>}据/span>质数是100吗?据/P.>据hr>
有据span class="katex"> ϕ据/span>(据/span>1据/span>0.据/span>0.据/span>)据/span>=据/span>(据/span>4.据/span>-据/span>2据/span>)据/span>(据/span>2据/span>5.据/span>-据/span>5.据/span>)据/span>=据/span>4.据/span>0.据/span>互质数到100据span class="katex"> {据/span>1据/span>那据/span>2据/span>那据/span>......据/span>那据/span>1据/span>0.据/span>0.据/span>}据/span>.据/span>
自据span class="katex"> G据/span>光盘据/span>(据/span>一种据/span>那据/span>B.据/span>)据/span>=据/span>G据/span>光盘据/span>(据/span>一种据/span>-据/span>B.据/span>那据/span>B.据/span>)据/span>那据/span>
G据/span>光盘据/span>(据/span>1据/span>0.据/span>1据/span>那据/span>1据/span>0.据/span>0.据/span>)据/span>=据/span>G据/span>光盘据/span>(据/span>1据/span>0.据/span>2据/span>那据/span>1据/span>0.据/span>0.据/span>)据/span>=据/span>⋮据/span>G据/span>光盘据/span>(据/span>2据/span>0.据/span>0.据/span>那据/span>1据/span>0.据/span>0.据/span>)据/span>=据/span>G据/span>光盘据/span>(据/span>1据/span>那据/span>1据/span>0.据/span>0.据/span>)据/span>那据/span>G据/span>光盘据/span>(据/span>2据/span>那据/span>1据/span>0.据/span>0.据/span>)据/span>那据/span>G据/span>光盘据/span>(据/span>1据/span>0.据/span>0.据/span>那据/span>1据/span>0.据/span>0.据/span>)据/span>.据/span>
因此,有据span class="katex"> ϕ据/span>(据/span>1据/span>0.据/span>0.据/span>)据/span>=据/span>4.据/span>0.据/span>互质数到100据span class="katex"> {据/span>1据/span>0.据/span>1据/span>那据/span>1据/span>0.据/span>2据/span>那据/span>......据/span>那据/span>2据/span>0.据/span>0.据/span>}据/span>.据/span>所以答案是据span class="katex"> 4.据/span>0.据/span>+据/span>4.据/span>0.据/span>=据/span>8.据/span>0.据/span>.据/span> □据/span>
求正整数的个数据span class="katex"> N据/span>≤据/span>1据/span>6.据/span>8.据/span>这样据span class="katex"> G据/span>光盘据/span>(据/span>N据/span>那据/span>1据/span>6.据/span>8.据/span>)据/span>=据/span>8.据/span>.据/span>
这些形式的正整数据span class="katex"> 8.据/span>m据/span>那据/span>在哪里据span class="katex"> m据/span>≤据/span>2据/span>1据/span>和据span class="katex"> G据/span>光盘据/span>(据/span>m据/span>那据/span>2据/span>1据/span>)据/span>=据/span>1据/span>.据/span>所以答案是据span class="katex"> ϕ据/span>(据/span>2据/span>1据/span>)据/span>=据/span>(据/span>3.据/span>-据/span>1据/span>)据/span>(据/span>7.据/span>-据/span>1据/span>)据/span>=据/span>1据/span>2据/span>.据/span> □据/span>
让据span class="katex"> N据/span>是一个正整数,然后找到据/P.>据P.>据strong>(一种)据/strong>小于的所有正整数的和据span class="katex"> N据/span>相对于据span class="katex"> N据/span>;据B.R.>据strong>(b)据/strong>小于的所有正整数的和据span class="katex"> 2据/span>N据/span>相对于据span class="katex"> N据/span>.据/P.>据hr>
(一种)据/strong>让据span class="katex"> S.据/span>价值据span class="katex"> D.据/span>据据/span>N据/span>那据/span>G据/span>光盘据/span>(据/span>D.据/span>那据/span>N据/span>)据/span>=据/span>1据/span>Σ据/span>D.据/span>和据span class="katex"> D.据/span>1据/span>据据/span>D.据/span>2据/span>据据/span>D.据/span>3.据/span>据据/span>......据/span>据据/span>D.据/span>ϕ据/span>(据/span>N据/span>)据/span>是小于的正数据span class="katex"> N据/span>相对于据span class="katex"> N据/span>.另外请注意,据span class="katex"> G据/span>光盘据/span>(据/span>D.据/span>那据/span>N据/span>)据/span>=据/span>1据/span>只有在据span class="katex"> G据/span>光盘据/span>(据/span>N据/span>-据/span>D.据/span>那据/span>N据/span>)据/span>=据/span>1据/span>.然后据span class="katex-display"> D.据/span>1据/span>+据/span>D.据/span>ϕ据/span>(据/span>N据/span>)据/span>=据/span>N据/span>那据/span>D.据/span>2据/span>+据/span>D.据/span>ϕ据/span>(据/span>N据/span>)据/span>-据/span>1据/span>=据/span>N据/span>那据/span>等等据/span>⟹据/span>S.据/span>=据/span>2据/span>N据/span>ϕ据/span>(据/span>N据/span>)据/span>.据/span>
(b)据/strong>我们必须找到据/P.>据P.>据span class="katex-display"> D.据/span>据据/span>N据/span>那据/span>G据/span>光盘据/span>(据/span>D.据/span>那据/span>N据/span>)据/span>=据/span>1据/span>Σ据/span>D.据/span>+据/span>N据/span>据据/span>D.据/span>据据/span>2据/span>N据/span>那据/span>G据/span>光盘据/span>(据/span>D.据/span>那据/span>N据/span>)据/span>=据/span>1据/span>Σ据/span>D.据/span>=据/span>S.据/span>+据/span>N据/span>据据/span>D.据/span>据据/span>2据/span>N据/span>那据/span>G据/span>光盘据/span>(据/span>D.据/span>那据/span>N据/span>)据/span>=据/span>1据/span>Σ据/span>D.据/span>=据/span>S.据/span>+据/span>D.据/span>据据/span>N据/span>那据/span>G据/span>光盘据/span>(据/span>D.据/span>那据/span>N据/span>)据/span>=据/span>1据/span>Σ据/span>(据/span>N据/span>+据/span>D.据/span>)据/span>=据/span>S.据/span>+据/span>N据/span>ϕ据/span>(据/span>N据/span>)据/span>+据/span>D.据/span>据据/span>N据/span>那据/span>G据/span>光盘据/span>(据/span>D.据/span>那据/span>N据/span>)据/span>=据/span>1据/span>Σ据/span>D.据/span>=据/span>2据/span>S.据/span>+据/span>N据/span>ϕ据/span>(据/span>N据/span>)据/span>=据/span>2据/span>N据/span>ϕ据/span>(据/span>N据/span>)据/span>.据/span>□据/span>
问题加载…据/P.>据P.class="note-text">注意加载......据/P.>据P.class="set-text">设置加载…据/P.>据/D.一世v>