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

7 votes
0 answers
316 views

Alternative approaches to Zudilin's proof of Apéry's theorem

The article Wadim Zudilin, Apéry's theorem. Thirty years after, Int. J. Math. Comput. Sci. 4 (2009), no. 1 pp 9–19. (arXiv:math/0202159, with the title An elementary proof of Apéry's theorem) in …
mamiladi's user avatar
  • 417
1 vote
1 answer
110 views

Question about arithmetic binomial coefficient

i have a question about the following assertion: let $n,j,u $ positive integer satisfying $ n \geq 5,$ $ 1\leq j \leq n-1$,$ \; n+1 \leq u \leq n+j$ let $ d[n]:=\operatorname{lcm}[1,2,..,n]$ t …
mamiladi's user avatar
  • 417
1 vote
0 answers
208 views

A question about a set of prime numbers

Let $n$ an integer sufficiently large. I'm looking for a "big" set $S$ of prime number $p$ satisfying $10.n \geq p > \sqrt{18n} $ and $p| C_{9.n}^{k-n}C_{8n+k}^{8.n}$ for all integer $k$ satifying $ …
mamiladi's user avatar
  • 417