8

Part of 2003 Iran MO (3rd Round)

Problems(1)

Italian TST 2004 - Problem 5

Source: Italian TST 2004 - Problem 5

A positive integer

n

is said to be a perfect power if

n=a^b

for some integers

a,b

b>1

(\text{a})

2004

perfect powers in arithmetic progression.

(\text{b})

Prove that perfect powers cannot form an infinite arithmetic progression.

inductionnumber theoryleast common multiplearithmetic sequencenumber theory proposed