比赛链接

AC 7题，Rank 9th

题意:

求解$(7+4\sqrt{3})^{n}$整数部分

题解:

$(7+4\sqrt{3})^{n}=x+y\sqrt{3},(7-4\sqrt{3})^{n}=x-y\sqrt{3}$

$0<(7-4\sqrt{3})<1,0<(7-4\sqrt{3})^{n}<1 \Rightarrow x,y\sqrt{3}整数部分相差不超过过1
又x \in N^{+},[y\sqrt{3}]=x-1,[(7+4\sqrt{3})^{n}]=2x-1$

$在Z(\sqrt{3})空间上快速幂即可$

by Hardict