Question

是否存在正整数a,b,c(a《b《c)使a的x次方=b的y次方=c的z次方=70的w次方≠1,1/w=1/x+1/y+1

Answer 1

由a^x=b^y=c^z=70^w得

xlog70(a)=ylog70(b)=zlog70(z)=w

则w/x=log70(a)

w/y=log70(b)

w/z=log70(c)

而1/x+1/y+1/z=1/w得w/x+w/y+w/z=1

即log70(a)+log70(b)+log70(c)=1

log70(abc)=1

故abc=70

由于abc都是正整数,a