MathOverflow

What is the asymptotic behavior of the coefficients of the series of the function$$\prod_{i\geq 0}\frac{1}{1 - x^{2^{i+1}-1}},$$which expressed the graded dimensions of homogeneous components of the Steenrod algebra $\mod 2$?

I am a junior high school student in Taiwan. I am trying to register for the written test of the National Taiwan University - Northern Taiwan High School Student Science Research Talent Cultivation Program - Mathematics Group. I have been hoping that...

Following the nice discussion on my previous prime-based Collatz variant, I have designed a new system that incorporates the total number of divisors $\tau(n)$ and the number of distinct prime factors $\omega(n)$.
Let $D(n)$ be defined for integers $n \ge 2$ as follows:...

Is there a version of the following result anywhere in the literature?
Proposition 1. Let $p\in\mathbb{Z}[n]$ satisfy $\deg(p)\geq2$, and let $\varepsilon>0$. Then there is $N\in\mathbb{N}$ such that the set $\{p(n);n\in\mathbb{Z}\}$ intersects at most $\varepsilon N$ residue classes mod $N$....