2005 IMO Problems/Problem 4
Problem
Determine all positive integers relatively prime to all the terms of the infinite sequence
Solution
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
See Also
2005 IMO (Problems) • Resources | ||
Preceded by Problem 3 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 5 |
All IMO Problems and Solutions |