Are both of these correct sentences: 「ここに住所を書いてくださいますか？」「ここに住所を書いてくださいませんか？」？

Question

I believe 「ここに住所を書いてくださいますか？」 means “Could you please write the address here?”

And 「ここに住所を書いてくださいませんか？」 means “Would you please write the address here?”

An exercise I’m doing shows the second sentence as the correct answer, but to my understanding both sentences are grammatically correct.

Am I right, or am I missing something?

Here’s the exercise, I have to choose what to fit in the gap to make a correct sentence.

ここに住所を書いて_______ か？

a. くださいます
b. くださいません

Answer 1

According to "A Dictionary of Basic Japanese Grammar" page 210:
"the negative question form makes a request more polite"

example:
明日八時に来てくださいませんか。
Would you please come at eight o'clock tomorrow?

But it doesn't say anything about the positive question form.

But the site below says that くださいますか is correct:
結論からいうと、「くださいますか」は日本語として正しいです。
https://www.rirekisyodo.com/study/doublehonorific-point.html

My guess is that your exercise was based on grammar books which still don't recognize the positive question form.