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Jan
11
revised Describe the rational points on $y^2 = 11 - 2x^3$
added 1353 characters in body
Jan
11
answered Describe the rational points on $y^2 = 11 - 2x^3$
Jan
11
comment Irreducibility of $x^4-5$ over $\mathbb{Z}_{17}$
I think your answer here is clearer than mine. Good.
Jan
11
answered Irreducibility of $x^4-5$ over $\mathbb{Z}_{17}$
Jan
11
comment Irreducibility of $x^4-5$ over $\mathbb{Z}_{17}$
But doesn’t this just show that $X^4-5$ has no root in $\Bbb F_{17}$?
Jan
11
comment Sum of the power series $\sum\limits_{n=2}^{\infty}\frac{n^2}{(n-1)(n+2)}x^n$
This is much more efficient than the method I was going to try.
Jan
11
comment Write and equation and justification to find $x$.
I think that the “justification” that a high-school teacher is looking for is the remark that the bisector divides the big angle into two equal smaller angles, $\angle ABD$ and $\angle DBC$.
Jan
11
comment What does this mean in English? (from math to English)
On the second line, “There is a unique $F$, mapping $P$ to $S$, such that”
Jan
10
comment Meaning of imaginary number
The usage is nowhere near consistent. One speaks of an “imaginary quadratic field”, even though only some of its elements are purely imaginary.
Jan
10
comment What is the intersection of $\mathbb Z$ with the ideal generated by $1-\zeta_n$?
Very pleasing explanation.
Jan
10
comment Calculate distance to person from camera if camera is on the floor
There are all sorts of photographico-mathematical objections to doing what you want, and I think your idea of using a comparison object would be much preferable. There’s the foreshortening of the body because the camera’s not looking at it straight-on; there’s the problem that the imaging of the camera will not be linear (objects at the edge of the field of view will be stretched), and probably more that I’m not thinking of right now.
Jan
9
comment Galois Group of a complex polynomial
This is excellent evidence that authors of textbooks can make mistakes just like you and me.
Jan
9
comment Solve the congruence $3x^2+x+8\equiv 0 \pmod{11}$
To discover the reciprocal of a number, just write down its powers modulo the modulus. The last power before you get to $1$ will be the reciprocal. So, modulo $11$, the powers of $3$ are $3$, $9$, $27\equiv5$, $15\equiv4$, $12\equiv1$, so that the reciprocal is $4$.
Jan
9
comment Calculate distance to person from camera if camera is on the floor
Do you know the camera’s field of view, in degrees for instance?
Jan
9
comment Solve the congruence $3x^2+x+8\equiv 0 \pmod{11}$
I got $2$ and $5$.
Jan
9
comment Show that the angles satisfy $x+y=z$
Very neat indeed.
Jan
9
revised Proof that nonconstant polynomial cannot have the same value at all integer points
added 1113 characters in body
Jan
9
answered P-adic expansion of rational number
Jan
8
comment P-adic expansion of rational number
“Different expansions”: are you requiring that the coefficients $a_i$ in your expression $\sum_ia_ip^i$ should all be in the set $\{0,1,\cdots,p-1\}$? If yes, the expansion of any $p$-adic number is unique (unlike the expansions of real numbers). But if you allow coefficients in a set of cardinality $>p$, the expansion is not unique.
Jan
8
comment Find the minimal polynomial over a field
A useful fact to remember