## The 2018 South African Mathematics Olympiad — Problem 3

The final round of the South African Mathematics Olympiad will be taking place on Thursday, 28 July 2019. In the week leading up to the contest, I plan to take a look at some of the problems from the senior paper from 2018. A list of all the posts can be found here.

Today we will look at the third problem from the 2018 South African Mathematics Olympiad:

Determine the smallest positive integer whose prime factors are all greater than , and that can be expressed as with positive integers and .

In many number theory problems, it helps to consider the prime factors of the numbers involved, and in this problem we are in fact forced to do so because the question itself is about the prime factors of a number. When dealing with factors of a number or an expression representing some number, it of course helps to consider whether we can factorise the given expression.…