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comment Let $a,x \in \mathbb{Z}$ and $n \in \mathbb{N}$, suppose $ax \equiv 1 \mod n$. Prove $a$ is coprime to $n$.
I.e. $ax-nk=1$. Check en.wikipedia.org/wiki/B%C3%A9zout%27s_identity
May
12
comment Prove that the unit ball in $X$ is not compact
@MeesdeVries: Absolutely. Edited, thank you.
May
12
revised Prove that the unit ball in $X$ is not compact
added 15 characters in body
May
12
answered Prove that the unit ball in $X$ is not compact
May
11
comment Proving function is $C^k$
Note that when $n=1$, $f$ even means that $f(x)=f(\mid x\mid)$.
May
11
answered Multiplication modulo 10 in Cayley's Table
May
11
comment Multiplication modulo 10 in Cayley's Table
You are. This is the table of the multiplication between invertible integers mod 10
May
11
comment Multiplication modulo 10 in Cayley's Table
$3\cdot7=2\cdot10+1=1\bmod 10$. What do you mean by "9 is the limit"?
May
11
comment Continuity of $\frac{1}{|x|}$ at $x= 0$
@5xum: you have a point there, but then I'd still prefer saying "0 does not belong to any domain for a function defined by the rule $x\mapsto\frac1{\mid x\mid}$" ... just to make clear what your point is.
May
11
comment What automorphisms exist on the abelian group of positive rationals under multiplication?
What about a generic permutation of the prime numbers?
May
11
comment Continuity of $\frac{1}{|x|}$ at $x= 0$
I am not the downvoter, but I would edit your second sentence saying "is not" instead of "cannot" and "the function" instead of "a function".
Apr
8
reviewed Reopen How to study math to really understand it and have a healthy lifestyle with free time?
Apr
8
reviewed No Action Needed If $K$ and $H$ are subgroups of $G$ and $H \triangleleft K$ then $K \subseteq N(H)$.
Apr
8
reviewed Leave Open Show that $\mathbb{Z}$ and $2\mathbb{Z}$ are not isomorphic as rings.
Apr
8
answered What is the difference between ring homomorphism and module homomorphism?
Mar
23
comment Prove that $|H|$ is odd and $|G/H|$ = $2^n$ for some positive integer n
Using Cauchy for 1 is overkilling! Pair elements with their inverses. Since $1_G$ is paired with itself a parity check shows immediately that there must be an other element paired with itself. For 2, yes, $\bar g=gH\in G/H$.
Mar
23
revised Prove that $|H|$ is odd and $|G/H|$ = $2^n$ for some positive integer n
deleted 2 characters in body
Mar
23
answered Prove that $|H|$ is odd and $|G/H|$ = $2^n$ for some positive integer n
Mar
23
awarded  Nice Answer
Mar
20
answered Show that $a - b \mid f(a) - f(b)$