Difference between revisions of "2005 Canadian MO Problems/Problem 5"

Revision as of 19:33, 28 July 2006

Problem

Let's say that an ordered triple of positive integers $(a,b,c)$ is $n$ -\emph{powerful} if $a \le b \le c$ , $\gcd(a,b,c) = 1$ , and $a^n + b^n + c^n$ is divisible by $a+b+c$ . For example, $(1,2,2)$ is 5-powerful.

Determine all ordered triples (if any) which are $n$ -powerful for all $n \ge 1$ .
Determine all ordered triples (if any) which are 2004-powerful and 2005-powerful, but not 2007-powerful.

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Difference between revisions of "2005 Canadian MO Problems/Problem 5"

Revision as of 19:33, 28 July 2006

Problem

Solution

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Revision as of 17:53, 28 July 2006 (view source) Chess64 (talk \| contribs)	Revision as of 19:33, 28 July 2006 (view source) Chess64 (talk \| contribs) m (2005 Canadian MO/Problem 5 moved to 2005 Canadian MO Problems/Problem 5) Newer edit →
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