1967 IMO Problems/Problem 3
Let be natural numbers such that is a prime greater than Let Prove that the product is divisible by the product .
We have that
and we have that
So we have that We have to show that:
is an integer
But is an integer and is an integer because but does not divide neither nor because is prime and it is greater than (given in the hypotesis) and .
The above solution was posted and copyrighted by Simo_the_Wolf. The original thread can be found here: 
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