Let r{x) be the product of all distinct primes dividing a nonzero integer x. The aèoconjecture says that if a, b, c are nonzero relatively prime integers such that a + b + c = 0, then the biggest limit point of the numbers logmax(|a|, |¿|, \c\) \o%r{abc) equals 1. We show that in a natural anologue of this conjecture for n > 3 integers, the largest limit point should be replaced by at least 2n-5. We present an algorithm leading to numerous examples of triples a, b, c for which the above quotients strongly deviate from the conjectural value 1.
Abstract. The aim of this paper is to study sequences of integers for which the second differences between their squares are constant. We show that there are infinitely many nontrivial monotone sextuples having this property and discuss some related problems.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.