Questions tagged [comp-number-theory]

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19
votes
4answers
640 views

How to obtain the unknown values $a_i,b_j$ given an unordered list of $a_i-b_j\mod N$?

Can anyone help me with the following problem? I want to find some values $a_i,b_j$ (mod $N$) where $i=1,2,…,K, j=1,2,…,K $ (for example $K=6$), given a list of $K^2$ values that correspond to the ...
12
votes
0answers
265 views

Conditional density of primes

We have some theorems about the density of prime numbers, the most famous one is probably the prime number theorem. My question is about the density of primes when we choose random numbers from a ...
14
votes
1answer
710 views

Is there a quantum NC algorithm for computing GCD?

From the comments on one of my questions on MathOverflow I get the feeling that the question regarding GCD being in $\mathsf{NC}$ vs. $\mathsf{P}$ is akin to the question regarding Integer ...
13
votes
4answers
3k views

Computing the Mobius function

The Mobius function $\mu(n)$ is defined as $\mu(1)=1$, $\mu(n)=0$ if $n$ has a squared prime factor, and $\mu(p_1 \dots p_k)= (-1)^k$ if all the primes $p_1,\dots,p_k$ are different. Is it possible to ...
12
votes
1answer
826 views

Complexity class of this problem?

I am trying to understand to which complexity class the following problem belongs: Exponentiating Polynomial Root Problem (EPRP) Let $p(x)$ be a polynomial with $\deg(p) \geq 0$ with coefficients ...
4
votes
1answer
137 views

Solving a system of sums-of-powers polynomials

What is the complexity of calculating the values of the integers $x_i$, where $0 \leq x_1 < x_2 < \dots < x_k < n$, given only the values $s_m = \sum_{i=1}^k x_i^m$? for $1 \leq m \leq k$? ...
18
votes
3answers
2k views

Determinant modulo m

What are the known efficient algorithms for computing a determinant of an integer matrix with coefficients in $\mathbb{Z}_m$, the ring of residues modulo $m$. The number $m$ may not be prime but ...