# Tagged Questions

Questions on more advanced topics of number theory, such as quadratic residues, primitive roots, prime numbers, non-linear Diophantine equations, etc. Consider first if (elementary-number-theory) might be a more appropriate tag before adding this tag.

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### A test problem about algebraic integers in complex field

In a recent algebraic test, I meet this problem: Let R be the ring of algebraic integers in C, K is the field of algebraic numbers in C. Let a be an element of K such that the ring R[a] is ...
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### How large number does it take to give a counterexample in number theory? [on hold]

There are many hypotheses in number theory regardless of the truth. I want to know how large number it needs to show a counterexample of certain hypothesis and how large number super-computers can ...
### Can $\sqrt[n]{\sqrt{a}+\sqrt{b}}+\sqrt[n]{\sqrt{a}-\sqrt{b}}$ be an integer?
The number $\sqrt{a}+\sqrt{b}$ cannot be an integer if $a,b$ are integers such that $\sqrt{b}$ is not an integer. (In fact, this is true for any number of square roots, and I believe even for cube ...