For someone who is self-studying Mathematics, how much depth of understanding is it required to do a graduate level research on Number theory?

To give you my background, I have basic knowledge of differential equations and linear algebra. Lately, I have done reading the book Elementary Number Theory by Burton. I was fascinated by the subject. I would like to explore and understand deeper until I can do my own research but I feel so lost. I have no idea what to do next.

Any answer is strongly valued.

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