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That would be equivalent to $2(n-1) = k\varphi(n)$ and $n-1\ne k'\varphi(n)$ by Fermat's little theorem for composite numbers. The second condition is equivalent to being able to satisfy first with …

You can look at rt.representation-theory or automophic-forms questions on Math Overflow. Here are some that may be relevant: Definitions of Hecke Algebras Induction and Coinduction of Representation …

To me, "elementary" = in principle can be understood by a person who only knows high school math. Notes: The person can be assumed to be extremely smart or a genius. What to mean by high school ma …

What can be said about the polynomials $f\in\mathbb Q[x, y]$ which are nonnegative on $\mathbb R\times \mathbb R$? Motivation: this may lead to progress in the question about polynomial onto map …

Class number $h(K)$ is exactly the quantitative measure of the failure of unique factorization: by its definition it measures "how many more ideas are there compared to numbers". To clarify: decompo …

Well, the numbers cannot be more then something like 10^5, so a simple program that cycles through all possible a and b and sees if there's a corresponding c might give you an answer pretty fast -- I …

What you're asking is (or will be after a slight change of question) essentially a form of "what's the smallest number that cannot be written in words" paradox.

I'm sure you omitted this just because it's too classic: big part of group theory was invented to prove that most algebraic numbers cannot be constructed by radical extensions. It's still the best, …

I'm somewhat familiar with base change in scheme theory: sometimes a property of a morphism X \to Y survives a base change f:Z\to Y, meaning that X \times_{Y} Z \to Z also has this property. Quest …

I believe there was an old conjecture that there's always a prime number between N and 2N. What's the history and how is this proven is the easiest/elementary/deepest ways?

Is it known that for every epsilon there is N_0 such that all intervals of the form [N, (1+\epsilon)*N], where N > N_0, contain prime numbers?

It's well-known that every natural number can be written as a sum of 4 squares of integers. Has there been any recent progress about the similar problem for the cubes, 4-th powers and so on? I believ …

There are several related questions here, the latter being especially interesting. We know the classical Eisenstein series. What are the Eisenstein series on a group G and why they are interesting? …

Trying to understand answer to this question. What is the (Beilinson) higher regulator of a number field?

I thought that the order of the Tate-Shafarevich group should always be a square (it's also supposed to be finite, but for the purposes of this question let's assume we know this) but I don't seem to …