# Tagged Questions

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### Any Computational Number Theory Book, include software programs for key steps of the proofs of major theorem?

All: Can anyone recommend some Computational Number Theory Books, which include software programs for key steps of the proofs of major theorem ? Some computational number theory books only include ...
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### Summation and product over $k$ with $k$ prime to $n$ sought

I just come to a standstill with the following two formulas. If $$E_n=\lbrace k\mid 1\le k\le n\ \&\ (k,n)=1\rbrace$$ then I hope for a closed formula $f(n)$ for those $$\sum_{E_n}k$$ ...
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### Help with proof regarding degrees of polynomials

How do you prove that if $f(x)\mid g(x)$ in $F[x]$, then either $g(x) = 0$ or $\deg(g(x)) \geq \deg(f(x))$ I'm not really sure how to prove these types of statements
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### Irrational to power of itself is natural

I've been thinking about a natural number like $n$ so that $x^x=n$ for some irrational $x$ but i couldn't find anything. As i didn't know how to approach the problem at all, i tried to make some ...
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### Lower bound on divisors of $\Phi_n(n)$

Take the nth cyclotomic polynomial $\Phi_n(x)$ and let $\phi$ be the Euler totient function. I can prove that all divisors $d$ of $\Phi_n(n)$ are such that $d \ge \phi(n)$ or $d = 1$. The proof is ...
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