MathDB
Always divisible by 10

Source: Ukrainian Mathematical Olympiad 2021. Day 1, Problem 8.1

December 20, 2023
number theorypolynomial

Problem Statement

It is known that for some integers a2021,a2020,…,a1,a0a_{2021}, a_{2020}, \ldots , a_1 , a_0 and any positive integer nn, the expression a2021n2021+a2020n2020+…+a1n+a0a_{2021}n^{2021} + a_{2020}n^{2020} +\ldots +a_1n + a_0 is divisible by 1010. Is it necessary that each of the numbers a2021,a2020,…,a1,a0a_{2021}, a_{2020}, \ldots , a_1 , a_0 is also divisible by 1010?
Back to ProblemsView on AoPS