Yeah, I don't think we actually disagree here... all I was saying is that there are proofs which are genuinely non-constructive, and this isn't one.
You are arguing that this usage of "constructive" is basically meaningless for statements like this. It could only make a difference for artificial examples or artificially complicated proofs. This is definitely true.
To be honest, I shouldn't have brought this up in the first place. I know what the author meant by claiming the proof is non-constructive (it doesn't give a formula for computing x,y such that x^2 + y^2 = p), and this is the idiomatic usage of the word non-constructive for this particular field. It's just different from the rest of the world, but that's nothing new.
You are arguing that this usage of "constructive" is basically meaningless for statements like this. It could only make a difference for artificial examples or artificially complicated proofs. This is definitely true.
To be honest, I shouldn't have brought this up in the first place. I know what the author meant by claiming the proof is non-constructive (it doesn't give a formula for computing x,y such that x^2 + y^2 = p), and this is the idiomatic usage of the word non-constructive for this particular field. It's just different from the rest of the world, but that's nothing new.