1209. Sequence Sum Possibi

TAG 数论

简单的数学题。设 n+.. +(n+k)=X， n>0,k>0

有 (2n+k)(k+1)=2X

k(k+1) <2X

k^2<2X

k<sqrt(2X)

枚举k到sqrt(2X)就行了

/* source code of submission 421009, Zhongshan University Online Judge System */ #include <stdio.h> #include <math.h> int T; int no,n; int cal(int n) { int ret=0; for (int i=1; i<=int( sqrt(2.0)*sqrt(n+0.0) ); ++i) { if ( (2*n)%(i+1)==0 && (2*n/(i+1)-i) >=2 && (2*n/(i+1)-i)%2==0 ) { ++ret; } } return ret; } int main(int argc, char *argv[]) { scanf("%d", &T); while ( T-- ) { scanf("%d%d", &no, &n); printf("%d %d/n",no, cal(n) ); } return 0; }