2012 USAMO Problems/Problem 3
Problem
Determine which integers have the property that there exists an infinite sequence
,
,
,
of nonzero integers such that the equality
holds for every positive integer
.
Solution
For any odd prime , the sequence
, where
is the greatest power of
that divides
, gives a valid sequence. Therefore, the set of possible values for
is at least the set of odd primes.
See Also
2012 USAMO (Problems • Resources) | ||
Preceded by Problem 2 |
Followed by Problem 4 | |
1 • 2 • 3 • 4 • 5 • 6 | ||
All USAMO Problems and Solutions |