MathDB

Let

a,b

be integers greater than 2. Prove that there exists a positive integer

k

and a finite sequence

n_1, n_2, \dots, n_k

of positive integers such that

n_1 = a

n_k = b

, and

n_i n_{i+1}

is divisible by

n_i + n_{i+1}

for each

i

(

1 \leq i < k

10