MARÍN SÁNCHEZ , Juan Manuel

F whic or h ev is ery p balanced, ositive in i.e., teger whose n ≡ 0 asso mod ciated 4, we Steinhaus construct a triangle zero-sum contains {±1} as man -sequence y +1's of as length 1's. n This implies the existence of balanced binary sequences of every length m 0 or 3 mo − d 4, ≡ thereby providing a new solution to a problem posed by Steinhaus in 1963.

In this paper we compute the Frobenius number of certain Fibonacci numerical semigroups, that is, numerical semigroups generated by a set of Fibonacci numbers, in terms of Fibonacci numbers.

A set A of integers is weakly sum-free if it contains no three distinct elements x, y, z such that x + y = z. Given k ≥ 1, let WS(k) denote the largest integer n for which {1, . . . , n} admits a partition into k weakly sum-free subsets. In 1952, G.W. Walker claimed the value WS(5) = 196, without proof. Here we show WS(5) ≥ 196, by constructing...