Filip Najman

activity

20102026

most citedGrowth of torsion groups of elliptic curves upon base change

38 citations · 186 across the 31 of their papers we have counts for

collaborators

Showing 2010Show all

5 papers · 1 filter

math.NT2010

Smooth values of some quadratic polynomials

Filip Najman

In this paper, using a method of Luca and the author, we find all values $x$ such that the quadratic polynomials $x^{2} + 1,$ $x^{2} + 4,$ $x^{2} + 2$ and $x^{2} - 2$ are 200-smooth and all values…

math.NT2010

On the largest prime factor of $x^{2} - 1$

Florian Luca, Filip Najman

In this paper, we find all integers $x$ such that $x^{2} - 1$ has only prime factors smaller than 100. This gives some interesting numerical corollaries. For example, for any positiv…

math.NT2010★ 1 cited

The Diophantine equation $x^{4} \pm y^{4} = i z^{2}$ in Gaussian integers

Filip Najman

In this note we find all the solutions of the Diophantine equation $x^{4} \pm y^{4} = i z^{2}$ using elliptic curves over $Q (i)$ . Also, using the same method we give a new proof of H…

math.NT2010

Complete classification of torsion of elliptic curves over quadratic cyclotomic fields

Filip Najman

In a previous paper, the author examined the possible torsions of an elliptic curve over the quadratic fields $Q (i)$ and $Q (- 3)$ . Although all the possible t…

math.NT2010★ 2 cited

Torsion of elliptic curves over quadratic cyclotomic fields

Filip Najman

In this paper we study the possible torsions of elliptic curves over $Q (i)$ and $Q (- 3)$ .

Smooth values of some quadratic polynomials

On the largest prime factor of x2−1

The Diophantine equation x4±y4=iz2 in Gaussian integers

Complete classification of torsion of elliptic curves over quadratic cyclotomic fields

Torsion of elliptic curves over quadratic cyclotomic fields

On the largest prime factor of $x^{2} - 1$

The Diophantine equation $x^{4} \pm y^{4} = i z^{2}$ in Gaussian integers