Squares in Lehmer sequences and some Diophantine applications
Squares in Lehmer sequences and the Diophantine equation Ax⁴ - By² = 2
Squares in Lucas sequences with rational roots.
Squares in products from a block of consecutive integers
Squares in products in arithmetic progression with at most one term omitted and common difference a prime power
Squares in products with terms in an arithmetic progression
Stabilität bei symmetrischen h-Basen
Stickelberger subideals related to Kummer type congruences
Study of rational cubic forms via the circle method [after D.R. Heath-Brown, C. Hooley, and R.C. Vaughan]
Sulla ricerca delle soluzioni intere di un tipo notevole di equazioni diofantee
Sums of k-th powers in the ring of polynomials with integer coefficients
Sums of like powers and some dense sets.
Sums of Squares Coprime in Pairs
Asymptotic formulae are provided for the number of representations of a natural number as the sum of four and of three squares that are pairwise coprime.
Sums of the form modulo a prime.
Sums of two k th powers.
S-unit equations over number fields.
Superelliptic equations arising from sums of consecutive powers
Using only elementary arguments, Cassels solved the Diophantine equation (x-1)³ + x³ + (x+1)³ = z² (with x, z ∈ ℤ). The generalization (with x, z, n ∈ ℤ and n ≥ 2) was considered by Zhongfeng Zhang who solved it for k ∈ 2,3,4 using Frey-Hellegouarch curves and their corresponding Galois representations. In this paper, by employing some sophisticated refinements of this approach, we show that the only solutions for k = 5 have x = z = 0, and that there are no solutions for k = 6. The chief innovation...
Superelliptic Equations of the form y^p=x^kp+a_(kp-1)x^(kp-1)+...+a_0
Sur certains nombres complexes compris dans la formule.
Sur des équations diophantiennes généralisant celle de Markoff