Difference between revisions of "2001 USAMO Problems/Problem 5"
(New page: == Problem == Let <math>S</math> be a set of integers (not necessarily positive) such that (a) there exist <math>a,b \in S</math> with <math>\gcd(a,b) = \gcd(a - 2,b - 2) = 1</math>; (b...) |
(No difference)
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Revision as of 02:38, 21 December 2008
Problem
Let 
be a set of integers (not necessarily positive) such that
(a) there exist 
with 
;
(b) if 
and 
are elements of (possibly equal), then 
also belongs to .
Prove that is the set of all integers.
Solution
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See also
| 2001 USAMO (Problems • Resources) | ||
| Preceded by Problem 4 |
Followed by Problem 6 | |
| 1 • 2 • 3 • 4 • 5 • 6 | ||
| All USAMO Problems and Solutions | ||
