MathDB

Italian TST 2004 - Problem 5

Source: Italian TST 2004 - Problem 5

June 17, 2004

inductionnumber theoryleast common multiplearithmetic sequencenumber theory proposed

Problem Statement

A positive integer

n

is said to be a perfect power if

n=a^b

for some integers

a,b

with

b>1

(\text{a})

Find

2004

perfect powers in arithmetic progression.

(\text{b})

Prove that perfect powers cannot form an infinite arithmetic progression.