On numbers with a unique representation by a binary quadratic form
On Euler-von Mangoldt's equation
Linear recurrences as sums of squares
Towards Bauer's theorem for linear recurrence sequences
Consider a recurrence sequence of integers satisfying , where are fixed and a₀ ∈ -1,1. Assume that for all sufficiently large k. If there exists k₀∈ ℤ such that then for each negative integer -D there exist infinitely many rational primes q such that for some k ∈ ℕ and (-D/q) = -1.
Products of disjoint blocks of consecutive integers which are powers
The product of consecutive integers cannot be a power (after Erdős and Selfridge), but products of disjoint blocks of consecutive integers can be powers. Even if the blocks have a fixed length l ≥ 4 there are many solutions. We give the bound for the smallest solution and an estimate for the number of solutions below x.
On Alternatives of Polynomial Congruences
What should be assumed about the integral polynomials in order that the solvability of the congruence for sufficiently large primes p implies the solvability of the equation in integers x? We provide some explicit characterizations for the cases when are binomials or have cyclic splitting fields.
Twierdzenia Fermata różnej wielkości
-
Kto się boi bardziej, czyli współczynnik Arrowa-Pratta
-
On -convergence of sequences
Sign-changes of the Thue-Morse Fractal Function and Dirichlet L-Series.
Relations between polynomial roots
Relations between polynomial roots
Page 1