# Questions tagged [factoring]

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### Is Determining the Number of distinct Prime Factors Polynomial?

Our current understanding of prime factorization states that it is hard to solve. The problem asks us to find the list of prime factors for an integer. For example, 18's prime factors are 3, 3, and 2. ...
• 55
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### Progress towards a Polynomial time factoring algorithm?

This is probably insignificant, but I was messing around with polynomials, and found out that, if we have a number, n = pq that we want to factor, if we expand (k+1)^n -k^n - 1, mod n, the first ...
• 229
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### Is there an efficient algorithm to find whether an integer is a prime power?

There's a sentence in the current version of the Wikipedia page for Shor's algorithm which states: we can use efficient classical algorithms to check if $N$ is a prime power. No reference is provided ...
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### How to approximate big composite number factors?

There is a big 1024-bits number A that was obtained by multiplying two numbers B and C.Are there any ways to get first numerical digits of these numbers? How example: ...
46 views

• 23
1 vote
81 views

### Isomorphism of finite dimensional polynomial algebras over finite fields

For a prime power $q$, consider polynomials $f_1,f_2 \in \mathbb{F}_q[x]$. Then, do we have an efficient way of checking whether there exists an algebra isomorphism between: \frac{\mathbb{F}_q[x]}{\...
• 155
1 vote
408 views

### Proof Review: Integer Factorization is in NP

I want to prove that integer factorization is in NP I have a general idea of how to prove this, and was wondering if I could get a sanity check: I'll show it's in NP by using a non-deterministic TM ...
1 vote
236 views

### Converting Ambiguous Grammar G to LL(1)

So I am in the process of learning about LL(1) grammar and converting an ambiguous one into LL(1). I know how to figure out if a grammar (G) is ambiguous, however, I am having trouble converting it to ...
• 151
1 vote
92 views

### Is it possible to transform this grammar into LL(1)?

This is the original grammar: S -> ABe A -> ab | a | ϵ B -> b I did try left factoring and this is what I got: ...
• 111
382 views

### Complexity class of integer factorization

Is integer factorization confirmed to be an NP-complete problem? If not, then if one could transform IF into an equivalent problem which is already proved to be NP-complete, would it mean that IF is ...
• 105
132 views

### General number field sieve is slower then exhaustive search for 'small' numbers?

In an attempt to understand the efficiency of the GNFS, I've been looking at runtimes. The calculations seem to indicate the GNFS runs slower than exhaustive search for smallish n. For example: ...
• 471
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### Is the runtime for the general number sieve given in base 10, e or 2?

When the runtime of the GNFS is given as e^(64/9*b(log b)^2)^1/3, what base is the log? I'm assuming its e, but other options would obviously be 10 and 2.
• 471
1 vote
159 views

### Is the prime factorization problem not an instance of the change making problem?

When using as the set of coins all logarithms of the prime numbers or numbers in general, and when using the logarithm of the number to be factored. The problem is just finding the logarithms that can ...
• 217
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### Is there an alternative to full factorization for testing the Polya conjecture?

The Polya conjecture is a disproved conjecture that states over half the numbers less than any number has an odd number of prime factors. It first fails at $n = 906,150,257$, thus being a good example ...
8k views

### Complexity of finding factors of a number

I have come up with two simple methods for finding all the factors of a number $n$. The first is trial division: For every integer up to $\sqrt{n}$, try to divide by $d$, and if the remainder is $0$ ...
• 618
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### What is fastest algorithm for factoring out square from number

I have $n$-digit integer $N=a^2b$, $b$ is square-free. In other words, $a$ is maximal square which divides $N$. What is fastest known algorithm to find $a$? I can write algorithm of $O(n^2\sqrt{N})$ ...
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