A cellular automaton on a torus.
A characterization of minimal zero-sequences of index one in finite cyclic groups.
A characterization of sequences with the minimum number of k-sums modulo k
Let G be an additive abelian group of order k, and S be a sequence over G of length k+r, where 1 ≤ r ≤ k-1. We call the sum of k terms of S a k-sum. We show that if 0 is not a k-sum, then the number of k-sums is at least r+2 except for S containing only two distinct elements, in which case the number of k-sums equals r+1. This result improves the Bollobás-Leader theorem, which states that there are at least r+1 k-sums if 0 is not a k-sum.
A complete annotated bibliography of work related to Sidon sequences.
A congruence for the coefficients in a series for π
A Distribution Property of the Sequences of Lucas Numbers.
A function related to the rumor sequence conjecture.
A general notion of independence of sequences of integers.
A note on p-adic valuations of Schenker sums
A prime number p is called a Schenker prime if there exists n ∈ ℕ₊ such that p∤n and p|aₙ, where is a so-called Schenker sum. T. Amdeberhan, D. Callan and V. Moll formulated two conjectures concerning p-adic valuations of aₙ when p is a Schenker prime. In particular, they conjectured that for each k ∈ ℕ₊ there exists a unique positive integer such that for each nonnegative integer m. We prove that for every k ∈ ℕ₊ the inequality v₅(aₙ) ≥ k has exactly one solution modulo . This confirms the...
A search for Tribonacci-Wieferich primes
Such problems as the search for Wieferich primes or Wall-Sun-Sun primes are intensively studied and often discused at present. This paper is devoted to a similar problem related to the Tribonacci numbers.
A set of squares without arithmetic progressions
A special prime divisor of the sequence: .
An addition theorem on the cyclic group .
An analogue of the Erdős-Ginzburg-Ziv theorem for quadratic symmetric polynomials.
An improvement on Olson's constant for ℤₚ ⊕ ℤₚ
Asymptotic behavior of Pascal's triangle modulo a prime