Abstract

In this paper, we present and describe Vô Conjecture 10 (VC10), a statement concerning the existence of pairs of distinct odd integers a,b>2 with disjoint sets of prime factors, such that the number of distinct prime divisors appearing in a, b, and a^k+b^k equals a prescribed integer n>3. This conjecture extends investigations into the distribution of prime factors in power sums and related expressions, and connects to classical problems in number theory.