Words can't end in "n" in Portuguese (Brazilian or otherwise), so the "n" is replaced with an "m" with very few exceptions like pólen (polen). It's worth noting that in Portuguese we don't pronounce the ending "m" or "n" for that matter. In other words, your lips don't touch at the end of "dindim". Both the "n" and the "m" in that word only serve to turn the short i into a nasal i. Try pronouncing the word "inn" without letting your tongue move at all and you'll get the idea, if you're not familiar with the sound.

"N"s also can't come before "P" or "B", in which case they also get replaced by "m". This is true in Spanish as well, though the first rule isn't.

makes sense, so it's really exact reduplication, but represented with the orthographic constraints you describe. thanks :)

I may be wrong but I guess that we don't have any words in portuguese that ends with in or din.

In Brazillian portuguese, the only words ended with "n" are scientific names (neologisms?) with a latin radical, e.g. elétron, próton, nêutron, pólen, plâncton, necton, etc.

In European portuguese, while the above forms are also common, the alternatives "electrão, protão, neutrão" are often found.