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12h
revised Irreducibility of $X(X-3)(X-\alpha)(X-\beta) + 1$
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12h
revised Irreducibility of $X(X-3)(X-\alpha)(X-\beta) + 1$
added 13 characters in body; edited tags
12h
accepted Irreducibility of $X(X-3)(X-\alpha)(X-\beta) + 1$
12h
answered Irreducibility of $X(X-3)(X-\alpha)(X-\beta) + 1$
1d
reviewed Leave Closed Could someone please explain double-angle identities?
1d
revised A finite group which has a unique subgroup of order $d$ for each $d\mid n$.
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1d
revised A finite group which has a unique subgroup of order $d$ for each $d\mid n$.
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1d
answered A finite group which has a unique subgroup of order $d$ for each $d\mid n$.
2d
reviewed Leave Closed Urn problem with replacement where the amount of balls drawn is random
May
26
awarded  Revival
May
26
revised Irreducibility of $X(X-3)(X-\alpha)(X-\beta) + 1$
added 23 characters in body
May
26
reviewed Leave Closed Understanding the lookAt function
May
26
comment Irreducibility of $X(X-3)(X-\alpha)(X-\beta) + 1$
@user225222: This is the exact version which I found as an exercise. Yes, I agree that this question should be doable with less restrictive conditions. Maybe it is possible to characterize all irreducible polynomials $(x-\alpha)(x-\beta)(x-\gamma)(x-\delta) + 1\in\mathbb Z[x]$ with $\alpha,\beta,\gamma,\delta\in\mathbb Z$?
May
26
comment Irreducibility of $X(X-3)(X-\alpha)(X-\beta) + 1$
@MartinBrandenburg: No, they are not. But given the condition $\alpha,\beta \geq 3$, the only problematic case is $\alpha = \beta = 3$, which is easily excluded looking at the reduction modulo $2$. Otherwise, $g$ and $h$ coincide in at least three different values. By $\deg(g) = \deg(h) = 2$, this implies $g = h$.
May
25
revised Irreducibility of $X(X-3)(X-\alpha)(X-\beta) + 1$
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May
25
comment Irreducibility of $X(X-3)(X-\alpha)(X-\beta) + 1$
@user26857: Thank you for the pointer. So I guess it remains to show that the given polynomial is not a perfect square in $\mathbb Z[X]$.
May
25
asked Irreducibility of $X(X-3)(X-\alpha)(X-\beta) + 1$
May
25
answered How is $\mathrm{PGL}(V)$ a subgroup of $\mathrm{P\Gamma L}(V)$?
May
23
comment Divisibility of polynomials in a subfield of a field.
(+1) This is nice! Is the notion of goodness something completely genuine for this purpose, or does it show up in other contexts es well?
May
22
answered Divisibility of polynomials in a subfield of a field.