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May
3
answered Combinatorial Problem From Book
May
3
comment show the splitting field of polynomial
The splitting field does have degree $8$ over $\mathbb{Q}$. The comment above does not contradict that. I am assuming that your $a$ is my $\alpha$. Already $\mathbb{}(\alpha)$ has degree $4$ over $\mathbb{Q}$, and it is not all of our splitting field.
May
3
revised Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis.
added 10 characters in body
May
3
comment 2 Trains and Fly Problem. Find the number of trips made by the fly back and forth.
There are infinitely many back-and-forth trips.
May
3
comment 2 Trains and Fly Problem. Find the number of trips made by the fly back and forth.
Flies fly fast. The initial distance between the trains should be given.
May
3
comment Collections (families of sets) and powersets
The union is the union of all $X$ such that $X\in P(E)$, that is, of all $X$ such that $X\subseteq E$.
May
3
comment Show that if $p$ is a prime of the form $p=4n+1$, then we can solve $x^2\equiv -1\mod p$(with $x$ an integer).
We have $xy\equiv -1\pmod{p}$ if and only if $y\equiv-(x^{-1})\pmod{p}$, where $x^{-1}$ is the modular inverse of $x$.
May
3
answered Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis.
May
3
comment All finite abelian groups of order 1024
A cruel problem, I think there are $42$.
May
3
answered Discrete Math On inductions
May
3
revised Find the volume of the region under $1+x+x^5$ and above $[0,1]$ that is revolved around the y axis
added 68 characters in body
May
3
comment Prove that if $\gcd(a, n)=1$, then $n\mid a^k-1$ for some $k$
Since $a^{\varphi(n)}\equiv 1\pmod{n}$, we have that $n$ divides $a^{\varphi(n)}-1$. The end.
May
3
comment Prove that if $\gcd(a, n)=1$, then $n\mid a^k-1$ for some $k$
You should just say that we can take $k=\varphi(n)$. (And any multiple of $\varphi(n)$ will do. Often a $k$ substantially less than $\varphi(n)$ will do. If you do not yet have Euler's Theorem, you will need to use a different proof, say by considering $a,a^2,a^3,\dots$.
May
3
comment Is it possible to prove the axiom of infinity from the real number axioms?
The assertion that the Axiom of Infinity follows seems highly plausible, and interesting.
May
3
comment Is it possible to prove the axiom of infinity from the real number axioms?
If a first-order theory over a countable language has an infinite model, or even arbitrarily large finite models, then for any infinite cardinal $\kappa$ it has a model of cardinality $\kappa$.
May
2
revised Find the volume of the region under $1+x+x^5$ and above $[0,1]$ that is revolved around the y axis
deleted 2 characters in body
May
2
revised Find the volume of the region under $1+x+x^5$ and above $[0,1]$ that is revolved around the y axis
added 273 characters in body
May
2
answered Find the volume of the region under $1+x+x^5$ and above $[0,1]$ that is revolved around the y axis
May
2
comment About the calculation of decimal digits of series up to the nth digit
Yes, I was just pointing out that "correct decimal representation up to $\dots$ can have more than one meaning.
May
2
comment About the calculation of decimal digits of series up to the nth digit
It depends on what you mean by correct to the $10$-th digit. In fact $\pi/4$ is about $0.785398163397$. So the $10$-th digit is $3$. But note that the digits after that are $97$. So to be sure that $3$ is correct, you need to know that the error (if it is in the wrong direction) is $\lt 3\times 10^{-12}$. That means a much larger number of terms than the huge number of terms mentioned in the answers.