2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/137961We consider the equation $$ ab + cd = λ, \qquad a\in A, b \in B, c\in C, d \in D, $$ over a finite field $F_q$ of $q$ elements, with variables from arbitrary sets $ A, B, C, D \subseteq F_q$. The question of solvability of such and more general equations has recently been considered by D. Hart and A. Iosevich, who, in particular, proved that if $$ #A #B #C #D \gg q^3, $$ then above equation has a solution for any $λ\in F_q^*$. Here we show that using bounds of multiplicative character sums allows us to extend the class of sets which satisfy this property.Number TheoryCombinatorics11L40, 11T30text