# Tagged Questions

For questions related to 'elementary' proofs in a technical sense, which has nothing to do with the difficulty of the argument or result. A typical example would be 'elementary' proofs of the Prime Number Theorem, which avoid complex analysis. The tag is however not limited to this particular notion ...

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### How to prove this Gaussian Mixture theorem? (Fitting/Overfitting)

Note from OP: I gave up and reposted this Question with a Bounty on Cross Validated HERE. In certain applications, we approximate an unknown pdf by placing uniformly weighted Gaussian terms at each ...
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### Implicit constant in Tenenbaum's result

In his famous book 'Introduction to Analytic and Probabilistic Number Theory', Gérald Tenenbaum established the following result (Theorem III.3.5): Let $g$ be a positive multiplicative function and ...
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### A trivial application of Wilson's theorem to Brocard's Problem

Proposition: Let $W(1)$ be the set of all Wilson primes of order $1$ and suppose $n=p-1,$ where $p$ is a prime such that $p\notin W(1)$, then there are no integer solutions to the equation $$n!+1=m^2$$...
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### Prime divisors in a proof [closed]

See this paper. See the definition of$${s \brace r}$$ on the fourth page. Why does it follow that $p$ divides$${2n \brace 3n/2}$$ from$$\frac{3n}{4}<p\le \frac{4n}{5}?$$Also, the same situation ...
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### Is an irreducible ideal in $R$ also irreducible in $R[x]$?

Let $R$ be a commutative Noetherian ring and $I\subset R$ an ideal that is irreducible in the sense that if $I = J_1 \cap J_2$, then $I=J_1$ or $I=J_2$. Is (the ideal generated by) $I$ irreducible in ...
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### Are there infinitely many $k$ for which $\frac{\sigma(k)}{k}=n^p$ and $p$ is an odd prime? [closed]

I would like to know if there are infinitely many $k$ for which $$\sigma(k)/k=n^p$$ such that $m=k{n}^{p-1}$ with $m,n>0$ and $p$ is an odd prime? Note: $\sigma(\frac{m}{{n}^{p-1}})$ is the sum of ...
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### A congruence conjecture regarding $(r-s)^4-1 \equiv 0\!\pmod{4r^2s}$

Is the following conjecture true? Conjecture. If $r > s \ge 1$ are relatively prime integers such that $$(r-s)^4-1 \equiv 0\!\pmod{4r^2s}, \tag{1}$$ then $r-s = 1$ ...
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### searching for an elementary proof a complex analysis result

Given a function $g$ entire on the whole complex plane $C$, it is possible to find an entire function $f$ such that $f(z+1) -f(z)=g(z)$. The proof can be given using riemann surface,automorphy,...
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### On a remark of Tait on FLT for the exponent 3

This is one of those recreational questions that aren't really about research. I found a curious remark in an old volume of American Mathematical Monthly (1922) which I'll quote below: In the ...
I'm looking for references to (as many as possible) elementary proofs of the Weyl's equidistribution theorem, i.e., the statement that the sequence $\alpha, 2\alpha, 3\alpha, \ldots \mod 1$ is ...