1.PP1+...+PP7=m => P1P7+P2P6+P3P5+PP4=m,因此PP4=0时,m最小
答案为P4
2.P^24 -1 = (P^12+1)(P^6+1)(P^3+1)(P^3-1)
=(P^4+1)(P^8-P^4+1)(P^2+1)(P^4-P^2+1)(P+1)(P^2-P+1)(P-1)(P^2+P+1)
当P=46,P^24 -1可被 P-1=45,P+1=47整除,答案为B
3.两个形式证明a不等於0,否则b:a无解
因此,a+b=0,则b=1 (b:a=1与a+b=0矛盾),a=-1,因此三数为1,0,-1
a^1992+b^1997 = 1+1 = 2 为答案
4.三等分角C(90度),则角MCH=30,角BCH=30,角MCB=60,角CMH=60,
得CMB为等边三角,因CMH面积为K,CMB面积为2K
因M为中点,则CAM面积=CMB面积,因此ABC面积为4K