MathDB

13

Part of 2000 Baltic Way

Problems(1)

n must be a prime power

Source: Baltic Way 2000

12/17/2010
Let a1,a2,…,ana_1,a_2 ,\ldots, a_n be an arithmetic progression of integers such that i∣aii|a_i for i=1,2,…,n−1i=1, 2,\ldots ,n-1 and n∤ann\nmid a_n. Prove that nn is a prime power.
arithmetic sequencenumber theory proposednumber theory