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# Questions tagged [prime-factorization]

For questions about factoring elements of rings into primes, or about the specific case of factoring natural numbers into primes.

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### Have numbers of this form forced small factors?

Let $F_n$ be the $n$ th Fibonacci-number and define $$f(n):=F_{n^2}-F_n+1$$ For most integers $n>1$ , $f(n)$ has a small prime factor : ...
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### Set of natural numbers related to least common multiple

I have come across the following set in my research, and I am curious whether this has been studied before/if there is a reference for a related construction. Given a natural number $n$, let $S(n)$ be ...
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### Quadratic Sieve on the Gaussian Integers

Factoring a large Gaussian integer $z_0 = a+bi$ into Gaussian primes may be done by first factoring the norm $N(z_0) = a^2 + b^2$ over the integers, and then considering the factors of each integer ...
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### No. of ways of factorizing a number into three distinct factors

Question: Let m be the number of triplets (p,q,r) of positive integer such that p<q<r and pqr is the square of the product of primes between 2 to 19 (including), when m is divided by 100 what ...
1 vote
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### Are the Poulet-numbers of the form $k^2+1$ all squarefree?

A Poulet-number $n$ is a weak Fermat-pseudoprime to base $2$ , in other words a composite number $n$ with the property $$2^{n-1}\equiv 1\mod n$$ The first $34$ poulet-numbers of the form $k^2+1$ (...