MathDB

ASU 306 All Soviet Union MO 1981 product of consecutive naturals

Source:

July 23, 2019

Productnumber theoryconsecutive

Problem Statement

Let us say, that a natural number has the property

P(k)

if it can be represented as a product of

k

succeeding natural numbers greater than

1

.
a) Find k such that there exists n which has properties

P(k)

and

P(k+2)

simultaneously.
b) Prove that there is no number having properties

P(2)

and

P(4)

simultaneously