15,782 reputation
12042
bio website math.brown.edu/~lubinj
location Minnesota
age 78
visits member for 3 years, 3 months
seen 8 hours ago

Aged mathematician


8h
comment Is it possible to divide a cube into $5772$ cubes of varying sizes?
Very nice indeed. Is there a general statement on just which numbers $n$ have the property that a cube can be cut up into $n$ smaller cubes?
8h
comment The definition of p-adic numbers
The following sequence of integers is getting closer and closer ($2$-adically) to $1$: $3, 5, 9, 17, 33, 65,\cdots$. In fact, their limit is $1$ itself. Get the picture?
13h
comment Does $20$ really have three distinct factorizations in $\mathcal{O}_{\mathbb{Q}(\sqrt{-31})}$?
Very pleasing examples!
13h
comment Determine the integers $a$ such that the congruence $x^4 \equiv a \pmod p$ has a solution for $p = 7, 11, 13$
Yes, that’s it!
13h
answered $x=x^2$ in a sub group?
13h
comment Determine the integers $a$ such that the congruence $x^4 \equiv a \pmod p$ has a solution for $p = 7, 11, 13$
Yes. This is the discrete logarithm for $p=7$, but you can use it without thinking of it as logarithms.
13h
answered Can someone explain why $x^{\log(a)} = a^{\log(x)}$?
14h
answered Determine the integers $a$ such that the congruence $x^4 \equiv a \pmod p$ has a solution for $p = 7, 11, 13$
19h
comment Parametrization of solutions of diophantine equation $x^2 + y^2 = z^2 + w^2$
Thanks for this. If I’d essayed a response, it would’ve looked very similar.
19h
answered $P$-adic Numbers Least Close to One
23h
comment $P$-adic Numbers Least Close to One
You’re talking about $2$-adic integers only, right? You do realize that there are oodles of $2$-adic integers that aren’t in $\Bbb Z$, right? I’m not sure what an “arithmetic series” might be in this context. Finally, any “even” number (like zero) is a lot farther from $1$ than $3$ is.
23h
comment Parametrization of solutions of diophantine equation $x^2 + y^2 = z^2 + w^2$
It’ll help a lot to know how this problem arose [is it homework?]; what level of mathematics you’re familiar with; and what you’ve tried so far. In particular, do you know the parametrization of solutions of $x^2+y^2=z^2$? (By the way, the answer to whether it can be parametrized is Yes.)
1d
comment Computing the galois group of $x^3+3x+1$
You don’t need to “know” the roots, you just have to name them. Let the real one be $r$ and the complex ones be $\rho$ and $\bar\rho$. You know that complex conjugation interchanges the last two and leaves the first one fixed. But the group $A_3$ has no elements of period (order) two. So the other choice for the Galois group, $S_3$, has to be the right one.
1d
comment continous function s.t $ \int_{0}^{\infty} f(x) dx$ exist
Hard to read, for lack of TeX. Best to learn.
2d
comment How to apply modular division correctly?
@BillDubuque, the lack of understanding of congruence modulo a number as an equivalence relation seemed to be a big stumbling block for my students when I was teaching Algebra.
Jan
28
comment The divisibility of $a^p-1$ by $a-1$ and by $(a-1)^2$
The first one is high-school algebra: surely you’ve seen a factorization of $a^n-b^n$?
Jan
27
comment Identify the ring $\mathbb{Z}[x]/(2x)$
Righto. My first thought was to liken OP’s ring to the affine ring of the union of the two axes in $2$-space.
Jan
27
comment Mazur's theorem-abelian group of rational points of an elliptic curve
The proof of Mazur’s Theorem is not basic or elementary in any sense, and when it first appeared, it was considered a notable triumph. The special case you mention at the end may not be too hard to show.
Jan
27
answered Is there an obvious reason why $4^n+n^4$ cannot be prime for $n\ge 2$?
Jan
27
comment Evaluate the sum $x + \frac{x^3}{3} + \frac{x^5}{5} + … $
Mathematical mysticism says that since the corresponding series with alternating signs is the inverse tangent, this should be the inverse hyperbolic tangent.