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Results tagged with nt.number-theory
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user 4794
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
35
votes
Accepted
How to prove this polynomial always has integer values at all integers?
$$P_m(x)=\sum_{i=0}^{m}\sum_{j=0}^{m}\binom{x+j}{ j}\binom{x-1}{ j}\binom{j}{ i}\binom{m}{ i}\binom{i}{ m-j}\frac{3}{(2i-1)(2j+1)(2m-2i-1)}.$$
Our task is to show it takes integer values on integers. …
- 3,504
9
votes
Normalizer of SL_2(Z) in GL_2(R)
The normalizer in $SL_2(\Bbb R)$ is indeed $SL_2(\Bbb Z)$.
[See the comments by Yves Cornulier for the normalizer in $GL_2(\Bbb R)$.]
If $\pmatrix{a&b\\c&d}\in SL_2(\Bbb R)$ normalizes $SL_2(\Bbb Z) …
- 3,504
5
votes
Applications of finite continued fractions
Wim Hesselink posed a problem motivated by image processing of a discretized picture.
I found that it was helpful to consider the convergents in a continued fraction approximation
of rational numbers. …