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visits member for 4 years, 6 months
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The essence of mathematics lies precisely in its freedom. - Georg Cantor

Once you have experienced flight in mathematical skies, you will forever walk the Earth with your eyes turned skyward, for there you have been, and there you will always long to return.


3h
comment If $a^2$ divides $b^3$, then $a$ divides $b$.
Choose any $\,\alpha,\beta\,$ so $\,\beta < \alpha \le \frac{3}2\beta\ \ $
5h
comment Need Verification on a Modulus Proof
You should be explicitly mention the case analyis: $\,n = 4m+1\,$ so $\,m\,$ is even or odd, so $\ldots$. You also need to handle the (easier) converse (or make bidirectional (iff) deductions).
5h
comment GCD of 1: Prove set is Complete Residue System Proof
@ModdedBear My point was that a slight, natural change to your proof makes the argument more general.
5h
comment GCD of 1: Prove set is Complete Residue System Proof
@MeganLoure It's just a slight generalization.
5h
comment GCD of 1: Prove set is Complete Residue System Proof
Note that the proof generalizes from $\,\{0,1,\ldots,m\!-\!1\}\,$ to any complete residue system since we can instead use $\,j\not\equiv k\pmod{m}\,\Rightarrow\,m\nmid j-k,\,$ and it's a bit clearer that way.
6h
comment GCD of 1: Prove set is Complete Residue System Proof
Hint: it suffices to show the map $\,x\mapsto nx\,$ is $\,1\!-\!1\,$ (so onto), so a permutation of $\,\Bbb Z_m.\ $
8h
reviewed Leave Open Two ideals that agree in the completion
8h
comment Finding the Modular Multiplicative Inverse of a large number
This method is generally the easiest way to organize the Extended Euclidean Algorithm (to compute modular inverses).
10h
answered inversing using euclids algorithm
12h
revised Does Bezout's lemma work both ways.
added 8 characters in body
12h
revised Does Bezout's lemma work both ways.
added 196 characters in body
13h
revised Does Bezout's lemma work both ways.
edited body
13h
comment Does Bezout's lemma work both ways.
@Jared It works for that question, not this one.
13h
answered Does Bezout's lemma work both ways.
13h
reviewed Leave Open Symmetric and similar matrices
14h
answered Difficult proof about coprime and factors of numbers!
16h
answered What does an ideal generated by a subset look like?
16h
comment What does an ideal generated by a subset look like?
Presumably you are considering rings with $1.\,$ If not, you should state that.
17h
revised Is this mod equality true?
added 49 characters in body
17h
answered Is this mod equality true?