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Results tagged with nt.number-theory
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user 175
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
46
votes
7
answers
10k
views
Are some numbers more irrational than others?
Some irrational numbers are transcendental, which makes them in some sense "more irrational" than algebraic numbers. There are also numbers, such as the golden ratio $\varphi$, which are poorly approx …
- 1,823
28
votes
2
answers
5k
views
Is Furstenberg's topology useful?
It's hard not to be amused and perhaps even amazed when first encountering Furstenberg's clever "topological" proof that there are infinitely many primes. Closer inspection, however, reveals the disap …
15
votes
A little number theoretic game
Edit: I added code to compute the Nim values for the first $N$ positions of this game after the original post, as requested by @Timothy-Chow. Unfortunately my results don't match those given by @Peter …
- 1,823
239
votes
14
answers
76k
views
Have any long-suspected irrational numbers turned out to be rational?
The history of proving numbers irrational is full of interesting stories, from the ancient proofs for $\sqrt{2}$, to Lambert's irrationality proof for $\pi$, to Roger Apéry's surprise demonstration th …