Ending question. Spoilers

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I hadn't thought of that either....though it did seem that he chose him for a reason. Fukuhara definitely wanted Fumiya to "be natural" about calling him father / old man. And they were alone during that conversation. I just assumed that they were both filling a hole in the other. Fukuhara had lost a son and Fumiya had lost a son. It's possible though! Fukuhara did say that thing about how some fathers are interesting.

ugh why do all the responses say "Wow I hadn't thought of that?"
Is there that huge of a difference in translation???
Or were all these people not paying attention? How can you claim to love the movie if you weren't paying attention???
I can understand getting bored reading the subtitles and missing the conversation about the dead son... but the roller coaster scene had no dialogue! It can't get any more obvious that they wanted us to think this was a father/son thing.
And how is the father/son idea too much of a coincidence but possibly sleeping with the guy's wife not a coincidence??? They made it clear he didn't sleep with the wife, but it never was spelled out that they weren't father and son.
I'd like to think they were, but it's equally possible they were not and simply just filling that void in their lives with each other. Perhaps the book had a different perspective. I haven't read it so I don't know how vastly different the film was compared to the book.

The people you idolize wouldn't like you.

Of course they are not. If they were, it wouldn't be interesting at all. They are simply strangers who by chance get an opportunity to fill a void in each other's lives. From the very first encounter the debt collector finds out that the boy is parentless and seeing what a looser he is, he realizes quickly there is a connection between these two facts. His further actions are directed towards fixing things for the boy, which means not just giving him the money, but also teaching him some self-confidence - sometning only a father can do. For him personally this is the last thing he wants to do before going to prison, the final good deed (kind of paralleling his desire to have his favorite dish before turning himself in). That's the essence of the movie for me.

To weigh in, if they were father and son, what is the dead woman? Wouldn't that be his mother? The one who Fukuhara killed? Wouldn't Fumiya be upset that his father killed his mother? So upset that he wouldn't accept the 1 million yen from Fukuhara? He said that his mother abandoned him at some point. Wouldn't he make the connection then?

the reason i think they are father and son, even though the son doesn't realise it are below

The father only realised this when he takes the students ID, this is at the start of the film. The ID will have his dob and birthplace, this is why the debt collect followed him

Also, the girl in the hotel who may be his mum. Remember they didn't sleep with each other and she said she would never forget him. Also the kiss scene was very awkward, i think the woman realised then who it could be

As others have mentioned, its said he did have a son and the part on the roller coaster sort of cemented it.

The debt collector also asks personal questions like first kiss etc and wants to relive parts of his sons childhood he missed.

so the turning point in the whole film is when the debt collector takes the students ID, this makes the coincidence easier to understand, there are other things as well but i was half sleeping watching it last night, i may watch again if anyone comments on this