1979 IMO Problems/Problem 1
If and are natural numbers so thatprove that is divisible with .
We first write Now, observe that and similarly and , and so on. We see that the original equation becomes where and are two integers. Finally consider , and observe that because is a prime, it follows that . Hence we deduce that is divisible with .
The above solution was posted and copyrighted by Solumilkyu. The original thread for this problem can be found here: 
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