2005 IMO Problems/Problem 4
Determine all positive integers relatively prime to all the terms of the infinite sequence
Let be a positive integer that satisfies the given condition.
For all primes , by Fermat's Little Theorem, if and are relatively prime. This means that . Plugging back into the equation, we see that the value is simply . Thus, the expression is divisible by all primes Since we can conclude that cannot have any prime divisors. Therefore, our answer is only
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