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Results tagged with nt.number-theory
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user 121643
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
4
votes
Are there infinitely many positive integer solutions to $(3+3k+l)^2=m\,(k\,l-k^3-1)$?
Here is another way maybe simpler as it reveals a certain Pell-Fermat equation. I don't know the relation with the other answer but i did many restrictions to get the following infinite sequence of so …
- 785
0
votes
0
answers
182
views
A certain Pell Equation
Recently I came up with a positive solution $((x,y)\neq (\pm 1;0))$ to this diophantine equation
$$
x^2-\left(w^2(2^{n-2}p)^2+2^n(2^{n-2}p)\right)y^2=1,\qquad n\geq 2,
$$
where all variables are in $ …
- 785
1
vote
On a generating set of numerical semigroups of multiplicity three
Some way to do this is to say $S=\langle a,b,c\rangle=\langle 3,3k+1,3j+2\rangle$ then it is easy to see that $g(S)=k+j$. Now take a generator of $S$ it can not be less than $F(S)$ as in any case mod …
- 785