2

Part of 2011 Iran Team Selection Test

Problems(1)

n>=2, a_i are natural numbers; and an arithmetic progression

Source: Iran TST 2011 - Day 1 - Problem 2

Find all natural numbers

n

2

such that there exist

n

natural numbers

a_{1},a_{2},\ldots,a_{n}

such that they are not all equal, and the sequence

a_{1}a_{2},a_{2}a_{3},\ldots,a_{n}a_{1}

forms an arithmetic progression with nonzero common difference.

number theoryleast common multiplearithmetic sequencenumber theory unsolved