MathDB
Problems
Contests
International Contests
CentroAmerican
2016 CentroAmerican
5
5
Part of
2016 CentroAmerican
Problems
(1)
Irie numbers
Source: Centroamerican 2016, problem 5
6/21/2016
We say a number is irie if it can be written in the form
1
+
1
k
1+\dfrac{1}{k}
1
+
k
1
for some positive integer
k
k
k
. Prove that every integer
n
≥
2
n \geq 2
n
≥
2
can be written as the product of
r
r
r
distinct irie numbers for every integer
r
≥
n
−
1
r \geq n-1
r
≥
n
−
1
.
number theory