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Ch7, Ch2 Arithmetic Function, CH01 - Coggle Diagram
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Ch2 Arithmetic Function
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Def:
f is a arithmetic function<=> f的定義域是N
f is a multiplicative arithmetic function <=> gcd(a,b)=1時，f(ab)=f(a)f(b)
i.e.想知f(n)的質那知道f(p^t)就知f(n)的質了
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f 、F is a arithmetic function
- (Möbius Inversion Formula)
F(n) = Σ d|n;d>0 f(d) <=>f(n) = Σ d|n;d>0 F(d)μ( n/d ):
- F(n) = Σ d|n;d>0 f(d)
f is a multiplicative arithmetic function <=>F is a multiplicative arithmetic function
CH01
ax=b (mod m)
gcd(a,m)=d
有解if d l b
無解 if d l b不行
解的個數: d個
所有解:
已知x=c(mod m )是其中之一解
(1. 用d去除以整個式子得到的解就是c
- 輾轉相除德d=ak+ml =>b=akb/d+mlb/d=> b=akb/d(mod m) )
所有解 x=c+mt/d where t=0,1,...,d-1
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