All Questions
6
questions
1
vote
3
answers
92
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Finite Factors of Refactorable Numbers
This was just a question that I came up with while learning about refactorable numbers.
While looking through the sequence of refactorable numbers (1, 2, 8, 9, 12, 18....), I decided to look at the ...
- 171
1
vote
0
answers
77
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Prime Factors of a Primitive Element
Let $p \in \mathbb{Z}$ be a prime, and let $f(x) = px^n + \dots$ be an irreducible degree $n$ polynomial over $\mathbb{Z}$ with leading coefficient equal to $p$. Suppose that $f(x)$ has no repeated ...
- 2,726
1
vote
2
answers
1k
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Computing Integers' Prime Factorization Using the General Number Field Sieve
Recently, I have taken upon myself the task of writing an algorithm to compute the prime factorization of an integer. I am neither a mathematician nor a programmer/computers' engineer as an occupation,...
- 821
4
votes
3
answers
508
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Rings where divisors of $mn$ are product of divisors of $m$ and $n$; relation to UFDs
Using the fundamental theorem of arithmetic, it's easy to prove this proposition:
Proposition. Every divisor of $mn$ can be written as the product of a divisor of $m$ to a divisor of $n$.
My ...
- 2,327
11
votes
4
answers
29k
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Why perfect square has odd number of factors [closed]
can someone please describe me why only the perfect square has odd number of factors.why does other number not has odd numbers of factors? I understand it but don't find any mathmetical proof.Please ...
user100315
11
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2
answers
3k
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Factoring a number of complex integers?
Say you are given a number (ex: $377$) and you express it in a form that allows you to factor it over the complex integers:
Notice,
$377 = 16^2 + 11^2$
Thus:
$(16 + 11i) $ and $(16 - 11i)$
Are ...
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