Difference between revisions of "2001 USAMO Problems/Problem 5"

Revision as of 12:38, 4 July 2013

Let $S$ be a set of integers (not necessarily positive) such that

(a) there exist $a,b \in S$ with $\gcd(a,b) = \gcd(a - 2,b - 2) = 1$ ;

(b) if $x$ and $y$ are elements of $S$ (possibly equal), then $x^2 - y$ also belongs to $S$ .

Prove that $S$ is the set of all integers.

This problem needs a solution. If you have a solution for it, please help us out by adding it.

Revision as of 01:38, 21 December 2008 (view source) Minsoens (talk \| contribs) (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...)		Revision as of 12:38, 4 July 2013 (view source) Nathan wailes (talk \| contribs) Newer edit →
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	[[Category:Olympiad Number Theory Problems]]		[[Category:Olympiad Number Theory Problems]]
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2001 USAMO (Problems • Resources)
Preceded by Problem 4	Followed by Problem 6
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All USAMO Problems and Solutions