All Questions

We are currently investigating a problem involving number theory, an area outside our field of expertise. Let $n$ be a positive integer. Consider two pairs of integers $(j,k)$ and $(j′,k′)$ as ...

Given an integer $a$, I would like to build a table of entries $(p, \text{ord}_p(a))$, where $p$ runs over the prime numbers not dividing $a$ and not exceeding a fixed parameter $P$, and $\text{ord}_p(...

I have the following question. First, consider the following congruence for primes $p\geq 5$: $24x\equiv -1\;(\mbox{mod}\;p)$. The smallest $x$, that is, $1\leq x\leq p-1$ for which the above ...

Let $n$ be integer with unknown factorization. Assume factoring $n$ is inefficient. Let $a,b,c$ satisfy $a^2+b^2 \equiv c^2 \bmod{n}, 0 \le a,b,c \le n-1$. Is it possibly to lift the above ...

Erdős and his coauthors often wrote about problems relating to the densities of sets of multiples. I have a computational question about the same topic. I have a finite* set $A=a_1<\cdots<a_r$ ...