MathDB

a_{n+1} = a_n - n if a_n >= n , or a_{n+1} = a_n + n if a_n < n

Source: Netherlands - Dutch NMO 1973 p5

January 27, 2023

recurrence relationSequencealgebra

Problem Statement

An infinite sequence of integers

a_1,a_2,a_3, ...

is given with

a_1 = 0

and further holds for every natural number

n

that

a_{n+1} = a_n - n

a_n \ge n

and

a_{n+1} = a_n + n

a_n < n

. (a) Prove that there are infinitely many numbers in the sequence equal to

0

. (b) Express in terms of

k

the ordinal number of the

k^e

number from the sequence, which is equal to

0