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Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions

1 vote

Subsets of the integers which are closed under multiplication

To make Mark Sapir's answer more explicit, we can take the direct product of sets obtained from your second example. For instance, we can take $S = \{ x: \exists a \in A, b \in B: x =ab\}$ where $A = …
Acccumulation's user avatar
1 vote

How to show that the following function isn't a polynomial over Q?

"If $f(x)$ were defined as $(x−b_1) + (x−b_1)(x−b_2) + …,$ then this question is not so hard." Does taking the derivative of the given function get you to this simpler case? "At any particula …
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