已知正整数a、b、c、d满足等式a/c=b/d=ab+1/cd+1.证明a=c,b=d

设a／c=b／d=﹙ab＋1﹚／﹙cd＋1﹚=k,则：①a／c=k,∴a=ck,②b／d=k,∴b=dk,③﹙ab＋1﹚／﹙cd＋1﹚=k,将①②代入③化简得：﹙k－1﹚﹙cdk－1﹚=0,分两种情况讨论：⑴k－1=0,则k=1,∴a=c,b=d.⑵cdk－1=0,则k=1／cd,...