MathDB

2005 | a_n x a_{n+31} All-Russian MO 2005 Regional 10.5

Source:

August 26, 2024

number theoryArithmetic Progressiondivisibledivides

Problem Statement

Arithmetic progression

a_1, a_2, . . . ,

consisting of natural numbers is such that for any

n

the product

a_n \cdot a_{n+31}

is divisible by

2005

. Is it possible to say that all terms of the progression are divisible by

2005