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Why are diophantine equations defined as having integer-only
solutions? Is it merely so that those solutions that are integer-only
have a name?
It seems easy to find a "diophantine equation" whose
solutions are real or complex, as well as integer.
Is it then no
longer a diophantine equation?
I guess I'm trying to get at whether this is just a semantic
distinction or whether there is a deeper reason for the naming
convention.