MathDB

4

Part of 2012 Grand Duchy of Lithuania

Problems(1)

a_n + a_{n+1} + a_{n+m }= 0 for all bounded sequences of integers a_n

Source: 2012 Grand Duchy of Lithuania, Mathematical Contest p4 (Baltic Way TST)

10/3/2020
Let mm be a positive integer. Find all bounded sequences of integers a1,a2,a3,...a_1, a_2, a_3,... for which an+an+1+an+m=0a_n + a_{n+1} + a_{n+m }= 0 for all n∈Nn \in N.
algebraSequence