Problem

Source: Kyiv City MO 2022 Round 1, Problem 7.4

Tags: number theory



In some magic country, there are banknotes only of values $3$, $25$, $80$ hryvnyas. Businessman Victor ate in one restaurant of this country for $2024$ days in a row, and each day (except the first) he spent exactly $1$ hryvnya more than the day before (without any change). Could he have spent exactly $1000000$ banknotes? (Proposed by Oleksii Masalitin)