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

9 votes
3 answers
2k views

Is this a new Fibonacci Identity? [closed]

I have found the following Fibonacci Identity (and proved it). If $F_n$ denotes the nth Fibonacci Number, we have the following identity \begin{equation} F_{n-r+h}F_{n+k+g+1} - F_{n-r+g}F_{n+k+h+ …
user918212's user avatar
  • 1,087
16 votes
2 answers
1k views

Is it decidable whether two real algebraic irrationals generate the same extension of the ra...

For an algebraic number $\alpha$, let $f_\alpha$ denote its minimal polynomial. We can symbolically represent an algebraic number $\alpha$ by the tuple $$ (f_\alpha, x, y, r) \in \mathbb{Q}[x] \times …
user918212's user avatar
  • 1,087
5 votes
0 answers
180 views

Is there an effective way to compute the square root of an algebraic number?

For an algebraic number $\alpha$, let $f_\alpha$ denote its minimal polynomial. We can symbolically represent an algebraic number $\alpha$ by the tuple $$ (f_\alpha, x, y, r) \in \mathbb{Q}[x] \times …
user918212's user avatar
  • 1,087