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Results tagged with nt.number-theory
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user 9712
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
22
votes
2
answers
2k
views
Have all numbers with "sufficiently many zeros" been proven transcendental?
Any number less than 1 can be expressed in base g as $\sum _{k=1}^\infty {\frac {D_k}{g^k}}$, where $D_k$ is the value of the $k^{th}$ digit. If we were interested in only the non-zero digits of this …
- 435
3
votes
1
answer
508
views
Sequences satisfying gcd(S(x), S(y)) = S(gcd(x,y))
Consider the sequence S(x) = 2^x - 1. This sequence has two interesting properties:
a) If the GCD of S(x) and S(y) is S(gcd(x,y)), and
b) For any prime p, S(p-1) is divisible by p.
Property a follo …
- 435
0
votes
1
answer
830
views
Numbers whose powers approach integers [closed]
Let d(x) denote the distance from x to the nearest integer.
Are there any non-integral numbers X for which the sequence d(X), d(X^2), d(X^3), etc. converges to 0?
EDIT: Sorry, I forgot to exclude th …
- 435