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

Revision as of 18:54, 7 February 2007

Problem

Let's say that an ordered triple of positive integers $(a,b,c)$ is $n$ -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.

Solution

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@@ Line 11: / Line 11: @@
 ==See also==
 *[[2005 Canadian MO]]
+{{CanadaMO box|year=2005|num-b=4|after=Last Question}}
 [[Category:Olympiad Number Theory Problems]]

2005 Canadian MO (Problems)
Preceded by Problem 4	1 • 2 • 3 • 4 • 5	Followed by Last Question

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

Revision as of 18:54, 7 February 2007

Problem

Solution

See also