Originally Posted by Wolverine
I presume it could just be that Madara's body was strong and capable enough to handle Hashirama's cells due to his Uchiha DNA stemming from his lineage to the Rikudou Sennin.
Yeah, I figure that might be the case. However, if the Rikoudou Sennin passed on his Eye powers to his Elder son, then he should be able to independently activate the Rinnegan without the influence of the Younger son's DNA, since the Younger son most probably has the full power of the Rikudou Sennin's body. (Not so sure the correlation of energies between the two sons and their correspondence so I'm not gonna go there).
Not exactly. If you remember the flashbacks, the eldest son has a different eye pattern than the Rinnegan. KYF's right, in order to achieve their father's ocular power, their DNA must be combined. So, without both halves one cannot achieve the Rinnegan.