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comment A question about how polynomials simplify under substitution
The sequence of revisions in this post is confusing, and may have misled you, for which I am sorry. Note that in the example you give, the group $M_0$ contains the nonconstant polynomial $x_1-x_0$.
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revised Distribution of polynomials mod 1 using co-prime integers
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revised Floors of powers of reals, how much do the first few determine the next?
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revised Floors of powers of reals, how much do the first few determine the next?
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revised Floors of powers of reals, how much do the first few determine the next?
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answered Floors of powers of reals, how much do the first few determine the next?
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comment Generating primes via composition of polynomials
Joe, Thank you for explaining the lay of the land.
Dec
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comment Reducibility of polynomials maps
Yes. In fact $x^2+1$ does the job.
Dec
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comment Reducibility of polynomials maps
Do we actually know a non-linear polynomial $f(x)$ such that $f^n(x)$ is irreducible for all $n$?
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comment Reducibility of polynomials maps
Joro, I added a logic tag.
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revised Reducibility of polynomials maps
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comment Generating primes via composition of polynomials
@Terry Tao: Thanks for pointing out this connection. I wonder if there are any footholds in the study of orbits of polynomials mod $p$ as $p$ varies?
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asked Generating primes via composition of polynomials
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revised How Symmetric is Diophantine Approximation using Fractions with Square Denominators?
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comment Distribution of polynomials mod 1 using co-prime integers
Thank you. This looks like "the" way to do it. In terms of Farey fractions your idea is to trap $\alpha$ between succesive fractions $a/b$ and $c/d$ with large denominator. Coprimality is preserved by taking mediants $(a+kc)/(b+kd)$ but the values of $\alpha (b+kd)−(a+kc)$ will form an arithmetic progression with small common difference. Pity that this doesn't generalize (as far as I can see) to polynomials of degree greater than 1.