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∑i=1mϕ(i∗n)=ϕ(p)∗∑i=1m[gcd(i,p)==1]ϕ(i∗n/p)+∑i=1m[p|i]ϕ(i∗n)=ϕ(p)∗∑i=1m[gcd(i,p)==1]ϕ(i∗n/p)+∑i=1m[p|i](p∗ϕ(i/p∗n))=ϕ(p)∗∑i=1m[gcd(i,p)==1]ϕ(i∗n/p)+∑i=1m/p(p∗ϕ(i∗n))=ϕ(p)∗∑i=1m[gcd(i,p)==1]ϕ(i∗n/p)+∑i=1m/p(ϕ(i/p∗n))+∑i=1m[p|i]((p−1)∗ϕ(i/p∗n))=ϕ(p)∗∑i=1m[gcd(i,p)==1]ϕ(i∗n/p)+∑i=1m/p(ϕ(i/p∗n))+∑i=1m[p|i](ϕ(p)∗ϕ(i/p∗n))=ϕ(p)∑i=1m(i∗n/p)+∑i=1m/pϕ(i∗n)更多推荐
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