Questions on more advanced topics of number theory. Consider first if (elementary-number-theory) might be a more appropriate tag before adding this tag.

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3
votes
1answer
229 views
+50

Prove or disprove that there exists a unique positive integer sequence $\{a_{n}\}$ satisfying a condition

Question: Prove or disprove: there exists a unique positive integer sequence $\{a_{n}\}$ satisfying the following condition: $\forall m\in N^{+}$, there exists a unique integer sequence ...
4
votes
0answers
78 views
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Differences between large numbers with many factors has little factors

I apologise beforehand for the informality and lack of precision in this question but it is that way because it comes from only an intuition, nothing more than a heuristic argument. Say one has two ...
7
votes
3answers
367 views
+50

How does one attack a divisibility problem like $(a+b)^2 \mid (2a^3+6a^2b+1)$?

In my current line of investigation, I am running into [many] divisibility questions like the one in the title, i.e. $$ (a+b)^2 \mid (2a^3+6a^2b+1), \qquad(\star) $$ where $a > b \ge 1$ are ...