# Understand the problem

Given that the number is an integer where and are prime positive numbers, determine .

##### Source of the problem

Danube 2014

##### Topic

Number Theory

##### Difficulty Level

Easy

##### Suggested Book

An Excursion in Mathematics

# Start with hints

Do you really need a hint? Try it first!

First settle the case where are not all distinct. Also, .

From hint 1, it follows that .

Hint 2 implies that and all divide . If they are distinct, then . Clearly this is a very strong restriction as it is expected that .

Show that, if are not all equal to 2, then which is a contradiction. Hence the only solution is .

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