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Results tagged with nt.number-theory
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user 124943
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
9
votes
2
answers
1k
views
Sets of algebraic integers whose differences are units
Fix a natural number $n\ge2$. Can we find $n$ algebraic integers $a_1,\dots,a_n$ in the field of complex numbers such that $a_i-a_j$ is a unit for all $i\ne j$?
- 1,638
1
vote
In Galois theory, why solvable groups must have their quotient groups be Abelian?
A solvable group is, by definition, a group with a finite series of normal subgroups such that the successive factor groups are abelian. It is the content of the Fundamental Theorem of Galois Theory t …
- 1,638
2
votes
Binomial congruence modulo prime
If $a$ is equivalent to 3 mod 4 then $a\choose 2$ is odd and $a^2\choose 4$ is even. So the proposed congruence fails with $b=2$, $p=2$ and any such $a$.
- 1,638
4
votes