数论题：证明(a,[b,c])=[(a,b),(b,c)]

楼主，(a,[b,c])=[(a,b),(b,c)]是不对的。正确的是:(a,[b,c])=[(a,b),(a,c)] ，证明：(a,[b,c])=(a,bc/(b,c) )=(a,bc)/(a,(b,c))=(a,b)*(a,c)/(a,b,c)=(a,b)*(a,c)/((a,b),(a,c))=[(a,b),(a,c)]