1/a+1/b=1/5 (a+b)/ab=1/5令a+b=t,t为自然数,则ab=5ta,b是方程x^2-tx+5t=0的两正整数根.b=t-a代入ab=5ta(t-a)=5t(a-5)t=a^2t为自然数,a-5>0 a>5t=a^2/(a-5)=(a^2-5a+5a-25+25)/(a-5)=a+5+25/(a-5)要t为自然数,则25/(...