I think we discussed this already, but how can they be brothers if 

they don't 

share the same surname?

This one is very simple to answer.

Remember that when a marriage takes place in Japanese society, and 
the daughter wed is the heir to the family estate and holdings, then 
in order for the husband to gain ownership of the land and holdings, 
he must assume her surname.

Therefore, Genma could very well have been born Masaki Genma, and 
changed his name to Saotome Genma after marrying Nodoka.

It's not entirely impossible. 

____

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