PE#243 Resilience

题目链接

题意是找到一个phi(m)/(m-1) < 15499/94744,要求m最小。
$$
phi(n)=n*\prod_{n|p}(1-\frac{1}{p})
$$

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
vector<int> phi;
vector<int> prime;
void sieve(int n) {
phi.resize(n);
for (int i = 0; i < n; ++ i) phi[i] = i;
for (int i = 2; i < n; ++ i) {
if (i == phi[i]) {
prime.push_back(i);
for (int j = i; j < n; j += i) {
phi[j] = phi[j] / i * (i - 1);
}
}
}
}
ll get_phi(ll x) {
if(x < phi.size())return phi[x];
ll ans = x;
for(ll i=2; i*i<x; i++) {
if(x%i == 0) {
ans = ans/i*(i-1);
while(x%i==0)x/=i;
}
}
if(x!=1) ans=ans/x*(x-1);
return ans;
}
ll sol(ll a,ll b) {
ll now = 1;
for(int i=0;i<prime.size();i++) {
for(ll k=1;k<prime[i];k++) {
ll x = get_phi(now*k);
ll y = now*k-1;
if(x*b<y*a) return now*k;
}
now*=prime[i];
}
return 0;
}
void solve() {
int n = 1000000;
sieve(n);
cout << sol(15499, 94744) << endl;
}