# Tagged Questions

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### 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 $1 \leq m \leq k$? ...
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### What is necessary and/or sufficient requirement for a subring of a field to be computable? [closed]

As title asks, what is necessary and/or sufficient requirement for a subring of a field to be a computable ring? Conditions on either field or subring are fine.
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### Sieve Methods for Twin Primes - How to extract algorithm from formula

I am reading Cojocaru and Murty's Introduction to Sieve Methods and their Applications. They wait until Chapter 5 to discuss the Sieve of Eratosthenes for finding primes - and their version of it is ...
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### n irrational number whose digits are pseudo-random: conceptual mismatch?

Are there irrational numbers whose digits are considered pseudo-random? Both concepts seem to be mismatched as a pseudo-random number generator typically is periodic and therefore generates a ...
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### 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 ...
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### Using the de Bruijn sequence to find the $\lceil\log_2 v \rceil$ of an integer $v$

Sean Anderson published bit twiddling hacks containing the Eric Cole's algorithm to find the $\lceil\log_2 v \rceil$ of an $N$-bit integer $v$ in $O(\lg(N))$ operations with multiply and lookup. The ...
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### Is the primality problem with unary input NLOGSPACE-Hard?

Consider the language $L=\{1^n : n \text{ is prime}\}$. Is this language NLOGSPACE-Hard? The motivation for this question is that $L$ is a good candidate for reducing to other languages related to my ...
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### Complexity of higher order residues

Let $P$ be a prime. Given a number $a$, what is the computational complexity in establishing if $a$ is a cubic or higher order residue modulo $P$? Are there any good algorithms?
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### What algorithms do you know for beltway reconstruction? [closed]

I've faced the beltway reconstruction problem and I've developed a simple backtrack algorithm, what algorithms do you know for this problem? Beltway Reconstruction Problem: Assume there is a set of ...
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### 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 ...
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### 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 ...