All Questions
Tagged with integer-partitions factoring
8
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Factoring an integer $N$ using its random partition of length $3$
While working on this MSE question that I had posted, I wondered what would be a minimal base of numbers that we could work with the algorithm described in that question.
I conjectured that a ...
- 3,341
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1
answer
125
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Is there a pattern to the number of unique ways to sum to a number?
I don’t think there is a proper name for these so I will refer to them as “phactors”. Basically, a phactor is a way to sum up to a number using positive real integers that are non zero and not equal ...
- 478
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When looking for 3 factors of value $x$ - what can one say about the number range where the factors must be in?
I want to find the 3 positive integer factors of a given positive integer $x$, such as
$a \cdot b \cdot c = x$
What can I say in what integer number range $a$ and $b$ must be in? (Of course, $c$ is ...
- 101
4
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1
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Partitions of $2n$ and factorizations of $n$
Let $n$ be any positive integer.
Let $p_1,p_2,...,p_m$ be any positive integers such that no more than one of the $p_i$s is $1$ and $\prod_{i=1}^mp_i=n$.
Finally, let $s_1,s_2,...,s_m$ be any ...
- 2,646
2
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3
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Multiplication partitioning into k distinct elements
Let's say I have a list with the prime factors of a number $n$ and their corresponding exponents. Is there a formula to calculate how many multiplications with $k$ distinct factors of $n$ are possible?...
- 264
4
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1
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Which positive integers can be written in the following form?
I was investigating a generalisation of this problem and found that it reduced to finding where the expression $$\frac{p(p+2m+1)}{2}$$
is an integer, where $p\ge 2$ and $m \ge 0$.
Since exactly one of ...
- 17.3k
6
votes
2
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Find all ways to factor a number
An example of what I'm looking for will probably explain the question best. 24 can be written as:
12 · 2
6 · 2 · 2
3 · 2 · 2 · 2
8 · 3
4 · 2 · 3
6 · 4
I'm familiar with finding all the prime factors ...
- 169
6
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2
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578
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Is an algebraic formula for the number of cyclic compositions of n known?
From Wikipedia:
In January 2011, it was announced that Ono and Jan Hendrik Bruinier, of the Technische Universität Darmstadt, had developed a finite, algebraic formula determining the value of p(n) (...
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