41 citations · 198 across the 39 of their papers we have counts for
4 papers · 1 filter
On the asymptotic Fermat's Last Theorem over number fields
Mehmet Haluk Sengun, Samir Siksek
Assuming two deep but standard conjectures from the Langlands Programme, we prove that the asymptotic Fermat's Last Theorem holds for imaginary quadratic fields Q(\sqrt{-d}) with -…
On powers that are sums of consecutive like powers
Vandita Patel, Samir Siksek
Let be even, and let be a non-zero integer. We show that for almost all (in the sense of natural density), the equation $$ x^k+(x+r)^k+\cdots+(x+(d-1)r)^k=y…
A Mordell-Weil theorem for cubic hypersurfaces of high dimension
Stefanos Papanikolopoulos, Samir Siksek
Let be a smooth cubic hypersurface of dimension over the rationals. It is well-known that new rational points may be obtained from old ones by secant and tangent cons…
Perfect powers that are sums of consecutive cubes
Michael Bennett, Vandita Patel, Samir Siksek
Euler noted the relation and asked for other instances of cubes that are sums of consecutive cubes. Similar problems have been studied by Cunningham, Catalan, Gen…