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Jun
20
revised I was wondering, shouldn't the fraction $\frac {-2}{-1}$ be less than 1?
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Jun
20
revised Solve $x^8 \equiv 3 \pmod {13}$
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Jun
20
answered Solve $x^8 \equiv 3 \pmod {13}$
Jun
20
answered I was wondering, shouldn't the fraction $\frac {-2}{-1}$ be less than 1?
Jun
16
comment Solutions of $y^2 = \alpha$ in $\mathbb{F}_{19}$
In general, the problem of computing square roots modulo a prime is not trivial. Two standard algorithms for this are the algorithms of Tonnelli-Shanks and of Cipolla.
Jun
16
comment More numbers between $[0,1]$ or $[1,\infty)$?
Note that this is almost exactly the tangent function (modulo the fact that the line is not tangent to the circle). ;) Indeed, keeping in mind the visual aspect of the trigonometric functions is very useful.
Jun
16
revised More numbers between $[0,1]$ or $[1,\infty)$?
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Jun
16
comment More numbers between $[0,1]$ or $[1,\infty)$?
Right, I was a bit sloppy. I guess OP will happily ignore this technicality for now (otherwise there are many posts on this site asking precisely this question :) ).
Jun
16
comment More numbers between $[0,1]$ or $[1,\infty)$?
Yes, a characteristic of infinite sets is that an infinite set can have the same cardinality as one of its proper subsets. Ever heard of Hilbert's hotel?
Jun
16
answered More numbers between $[0,1]$ or $[1,\infty)$?
Jun
14
answered How to learn/speak “mathematical english”?
Jun
13
comment 1 is equal to -i
However, you could "prove" in the same way that $-i = i$. ;) The error basically is that $a^2 = b^2$ does not imply $a = b$ (unless you assume, for example, that $a$ and $b$ are positive real numbers).
Jun
13
comment Finding conjugacy classes
$(321)$ and $(132)$ are the same permutation.
Jun
13
answered Finding conjugacy classes
Jun
12
comment Courses, books or other resources specifically written to teach and help understand algorithmic language?
I have no idea what "algorithmic language" could possibly mean.
Jun
11
comment “As this holds for all values of $x$, then something is true” logic.
This is true in any ring with uniity: if $ax = bx$ is true for all $x$, then in particular it is true for $x = 1$.
Jun
10
comment Exactly one ring homomorphism $F[X] \rightarrow S$
Show that the two properties you are given completely determine $\phi$. In other words, there is only one possible value for $\phi(x)$, for all $x\in F[\alpha]$.
Jun
10
answered Prove that these two groups are isomorphic to each other.
Jun
10
comment Is every finite field a quotient ring of ${Z}[x]$?
If by "order" you mean "degree", then this is false as well. $\mathbf{F}_{p^k}$ is the quotient of $\mathbf{F}_p[x]$ by the principal ideal generated by an irreducible polynomial of degree $k$, not $k-1$.
Jun
9
comment Can I do research just because I am able to?
By the way, Academia.SE regularly sees questions very similar to yours, have you looked there?