MathDB

n must be a prime power

Source: Baltic Way 2000

December 17, 2010

arithmetic sequencenumber theory proposednumber theory

Problem Statement

Let

a_1,a_2 ,\ldots, a_n

be an arithmetic progression of integers such that

i|a_i

for

i=1, 2,\ldots ,n-1

and

n\nmid a_n

. Prove that

n

is a prime power.