MathDB

n_1 = a,n_k = b, (n_i + n_{i+1}) | n_in_{i+1}

Source: JBMO Shortlist 2007 A4

October 14, 2017

JBMOalgebrapositive integer

Problem Statement

Let

a

and

b

be positive integers bigger than

2

. Prove that there exists a positive integer

k

and a sequence

n_1, n_2, ..., n_k

consisting of positive integers, such that

n_1 = a,n_k = b

, and

(n_i + n_{i+1}) | n_in_{i+1}

for all

i = 1,2,..., k - 1

Back to Problems View on AoPS