# Tagged Questions

**8**

votes

**2**answers

509 views

### runs of consecutive non squarefree integers

This question gained no attention at Math SE.
Call a sequence of $k$ consecutive naturals squary if each one of them is divided by a square > 1. The Chinese Remainder theorem trivially guarantees us ...

**6**

votes

**1**answer

362 views

### Using the decomposition $641 = 5^4 + 2^4$ to factor $F_5$

The question in the title arises from a problem in Stewart's "Galois Theory, Third Edition" (and possibly elsewhere) which has been bugging me for a few days since reading it:
Problem 19.5 (p. 224) ...

**7**

votes

**3**answers

741 views

### $\omega(p^n - 1)$ as $n \rightarrow \infty$

Although I am also interested in the number of distinct prime factors (not counting
multiplicity), today I use $\omega(m)$ to denote the number of (positive) prime
factors (with multiplicity) of the ...

**8**

votes

**5**answers

1k views

### Polynomials all of whose roots are rational

I have two questions about the class of integer-coefficient polynomials all of whose roots are rational.
I asked this at MSE, but it attracted little interest (perhaps because it is not interesting!)
...

**5**

votes

**0**answers

506 views

### Is integer factorization harder than RSA ($n=pq$) factorization? [closed]

This is a repost. I could not get a precise answer on math.SE and cstheory.SE
Let FACT denote the integer factoring problem: given $n \in \mathbb{N},$ find primes $p_i \in \mathbb{N},$ and integers ...