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Nov
14
comment Determine $\phi(2^{399}+1)$
Intended answer: some very large number.
Oct
19
comment xy+x+y=0 What is the inverse Element?
@Clayton Your confusion arises from mixing up the two multiplication operations.
Oct
19
comment Excercise: Find the volume of the parallelepiped
In your formula, a, b, and c are not points. ;)
Sep
30
awarded  Explainer
Sep
24
awarded  Autobiographer
Sep
4
comment Bisectors problem
So it is just a hypothesis that N exists and B lies between M and N?
Sep
4
comment What is the flaw in this proof that all triangles are isosceles?
You read the statement somewhere, it would help us if you indicated where you read it.
Sep
3
comment Bisectors problem
That's what I guessed, chen h.; however consider a 45-45-90 triangle with legs AC, BC. Then the bisector of the supplementary angle of ACB is parallel to AB.
Sep
3
comment Bisectors problem
Just wondering, what is the supplementary angle of a given angle? I took a guess, but it does not always happen that B lies between M and N with my choice.
Sep
1
comment Right-adjoint to the inverse image functor
I discovered the right-adjoint $g$ by considering two simple examples. Let $f_1$ be the function from the set of two points to the singleton set. Let $f_2$ be the function $\{a,b,c\}\to\{u,v\}\colon a,b\mapsto u,c\mapsto v$. Perhaps these considerations will help you too.
Sep
1
comment question about $Spec(A)$ in Atiyah's book Introduction to Commutative Algebra
@claire Yep, there is no such thing as an infinite sum. We sometimes abuse notation and write $\sum_{i\in I}f_ig_i$, $g_i\in A$ and all but finitely many of the $g_i$ are zero.
Sep
1
comment question about $Spec(A)$ in Atiyah's book Introduction to Commutative Algebra
@claire You need to be a little more careful, since you may notice that your description allows for infinite sums in $A$ (something that makes no sense in your random ring $A$).
Sep
1
answered question about $Spec(A)$ in Atiyah's book Introduction to Commutative Algebra
Jul
16
comment Calculating a Factorial Base Representation
While it is hard to be more explicit in your statement of the algorithm, a proof of it would be nice (I have proven it myself--I am just suggesting an improvement for your answer)
Jun
27
comment Definition of relatively prime in UFD´s
BTW, it's great that you are comparing the definitions from two sources.
Jun
27
comment Definition of relatively prime in UFD´s
If it was not a Unique Factorization Domain, you would be 100% correct.
Jun
27
comment why is the answer 21,845 and not 218,450?
This is a great example indicating the value in estimating an answer prior to computing it. $5.47/6.26$ is larger than $5/7$ which is $0.7142857...>7/10$. So the true answer is greater than $7*25,000=175,000$.
Jun
26
comment Definition of irreducible element.
@Sodan I believe it is a mistake on the part of Ireland & Rosen. Cf. Corollary 1.3.2 to see an instance where they implicitly assume irreducible implies nonunit.
Jun
25
comment If $\mathbb{Z}$ satisfies an identity $\eta$, then every **commutative** ring satisfies $\eta$? And related questions.
Is it even true in $\mathbb Z$? :)
Jun
21
comment $ 7\mid x \text{ and } 7\mid y \Longleftrightarrow 7\mid x^2+y^2 $
I see an approach to the second implication involving the fact that every divisor of $x^2+y^2$ is a sum of two squares if $x$ and $y$ are relatively prime. Presumably it is considered too high-powered, but on the other hand it makes the generalization to primes other than $7$ obvious.