MathDB

Let

a_1,a_2, \cdots ,a_{2015}

2015

-tuples of positive integers (not necessary distinct) and let

k

be a positive integers. Denote

\displaystyle f(i)=a_i+\frac{a_1a_2 \cdots a_{2015}}{a_i}

.
a) Prove that if

k=2015^{2015}

, there exist

a_1, a_2, \cdots , a_{2015}

such that

f(i)= k

for all

1\le i\le 2015

.\\ b) Find the maximum

k_0

so that for

k\le k_0

, there are no

k

such that there are at least

2

different

2015

-tuples which fulfill the above condition.

Problem Statement