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I posted this question in MSE around a month ago, but didn't receive any suitable answers. So, I decided to give it a try here as well- I was trying to explain the famous proof of infinitude of primes …

The following question arose from a problem I am working on. Let $N, k$ be positive integers. Consider the Diophantine equation in $a, b, c$: $$ \frac{1}{a} + \frac{N - 1}{b} = \frac{N^k}{c} $$ with …

The interplay between ergodic theory and Number Theory owes a lot to the Abel Prize winner Hillel Furstenberg. So, I must suggest his book, Recurrence in Ergodic Theory and Combinatorial Number Theory …

I posted this question on MSE, and failed to get the type of answer I wanted. That's why I would like to post it here and wait for the experts to reply. Here's the link to the MSE post, which I anyway …

This question is mainly inspired from a different problem I was working on. Is there a value of $k$ such that, for each $n\in \mathbb N$, the equation $$\sum_{i=1}^{k}x_i^2=n$$ is solvable in $x_1,\do …

A set $\mathcal S$ of positive integers is called stable if for every fixed positive integer $d$, the relation $$n\in \mathcal S \iff dn\in \mathcal S$$ holds for almost all positive integers $n$. Typ …

We call a set of natural numbers $\mathcal S$ to be a Sidon Set if $a+b=c+d$ for $a,b,c,d\in \mathcal S$ implies $\{a,b\}=\{c,d\}$. In other words, all pairwise sums are distinct. Erdős conjectured th …

OEIS A169945 introduces the concept of thickness of a polynomial as the magnitude of the largest coefficient in the expansion of the square of the polynomial. Considering the $2^{n+1}$ polynomials $p( …

Call a set $\mathcal S \subset \mathbb N$ to be $(k,\ell)$-sumfree if there are no non-trivial solutions to the equation $$x_1+\dots +x_k = y_1+\dots +y_\ell$$ in the set (for distinct $x_i$'s and $y_ …

For a non-negative integer $s$, a strictly increasing sequence of positive integers $\{a_n\}$ is called $s$-additive if for $n>2s$, $a_n$ is the least integer exceeding $a_{n-1}$ which has precisely $ …

I was wondering about sets that do not contain any $3$-term AP, and came to know that the official name of such a set is Salem–Spencer set. I was considering the question of counting the number of Sal …