MathDB

(a_1+d) (a_2+d)... (a_n + d) / (a_1a_2...a_n) is integer for every d>=0

Source: Rioplatense Olympiad 2018 level 3 p5

December 11, 2018

number theoryIntegerProductProductspositive integers

Problem Statement

Let

n

be a positive integer. Find all

n

- rows

( a_1 , a_2 ,..., a_n )

of different positive integers such that

\frac{(a_1 + d ) (a_2 + d ) \cdot\cdot\cdot ( a_n + d )}{a_1a_2\cdot \cdot \cdot a_n }

is integer for every integer

d\ge 0