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Results tagged with nt.number-theory
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user 103119
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
1
vote
1
answer
132
views
How to solve the below simultaneouly Diophantine equations?
How to solve the simultaneous Diophantine equations:
$q=p^3+6m^2p-12m^3-12mp^2$,
$p=q^3+6m^2q-28m^3-28mq^2$
for rational numbers $p,q,m$?
1
vote
1
answer
240
views
Are there nontrivial rational solutions of $x^{n-m}=(1+t^m)/(1+t^n)$?
Let $n-m \ge 2$ be two fixed natural numbers. Are there any nontrivial rational solutions of the equation $$x^{n-m}=(1+t^m)/(1+t^n)$$ for $x$ and $t$? As particular cases the
rational solutions of t …
4
votes
2
answers
687
views
Rank of certain elliptic curves
I need to calculate rank of the some
elliptic curves,(espicially getting generators or finding a rational point
on the elliptic curves) but I cannot do this by my computer.
I am interested in c …