2001 IMO Problems/Problem 6
are positive integers such that . Prove that is not prime.
First, as and . Thus, .
Similarly, since and . Thus, .
Putting the two together, we have
Now, we have: So, we have: Thus, it follows that Now, since if is prime, then there are no common factors between the two. So, in order to have we would have to have This is impossible as . Thus, must be composite.
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