MathDB

Let

n_1,n_2,\ldots,n_s

be distinct integers such that

(n_1+k)(n_2+k)\cdots(n_s+k)

is an integral multiple of

n_1n_2\cdots n_s

for every integer

k

. For each of the following assertions give a proof or a counterexample:

(\text a)

|n_i|=1

for some

i

(\text b)

If further all

n_i

are positive, then

\{n_1,n_2,\ldots,n_2\}=\{1,2,\ldots,s\}.

B4