10.5

Part of 2005 All-Russian Olympiad Regional Round

Problems(1)

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

Source:

Arithmetic progression

a_1, a_2, . . . ,

consisting of natural numbers is such that for any

n

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

number theoryArithmetic Progressiondivisibledivides