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Results tagged with nt.number-theory
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user 9896
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
4
votes
Can finitely many values of a polynomial determine it?
This is not true. $f(x)$ and $f(2x)$ will not be in the same equivalence class in general, yet their images will agree on infinitely many points. Hence there is no fixed value $m$ such that any $m$ po …
- 3,475
7
votes
2
answers
725
views
How close to an integer can a polynomial root be?
Suppose I have a polynomial $p(x) = a_n x^n + ... + a_0$ where $a_n, \dots, a_0$ are integers. I would like to show that any root of this polynomial is either an integer or is far from an integer. Tha …
- 3,475