All Questions

I have a sequence of positive integers $a_n$ which assumes infinitely many times the value $1$. I want to estimate the cardinality of the following set: $$\#\{n\leq x : a_n>1 \text{ and } (a_n, \...

The integer partition function $p(n)$ has a generating function given by $$\frac1{(q)_{\infty}}=\sum_{n=0}^{\infty}p(n)q^n$$ with $(q)_{\infty}=\prod_{m=1}^{\infty}(1-q^m)$. The long-standing problem ...

Define $\triangle_n$ to be the $n$th triangular number. Define $$M_n=(2\triangle_n-1)2\triangle_n(2\triangle_n+1)=2\triangle_n(4\triangle_n^2-1).$$ Define $(\ell,k)$-smough numbers to be numbers that ...

It is possible to define a classification similar than the Erdös-Selfridge classification of primes for different sequences. Please ee [1], section A18 and the references cited in this book. Because ...

Let $A$ be a set of integers. In our recent researches, we've faced to the following property and definition: We say $A$ has infinite difference length, if (a) For every integer $n$ there exist a ...