Question

证明a,b为正整数,ab/(a+b)也为整数,则(a,b)>1

Answer 1

反证法，如果（a,b)= 1; 则有（a,a+b) = 1;(b,a+b) = 1;
=>(ab,a+b) = 1; 有因为ab/(a+b) 为整数，只能ab/(a+b) = 1;即a=b=2;矛盾
故（a,b) >1;