MathDB

Sequence of integers and prime numbers

Source: Netherlands IMO Team Selection Test 2013

October 21, 2014

number theoryprime numbersnumber theory unsolved

Problem Statement

Fix a sequence

a_1,a_2,a_3\ldots

of integers satisfying the following condition:for all prime numbers

p

and all positive integers

k

,we have

a_{pk+1}=pa_k-3a_p+13

.Determine all possible values of

a_{2013}