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a tricky equation (1^m)+(2^m)=(3^m

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a tricky equation (1^m)+(2^m)=(3^m [#permalink] New post 10 Jun 2004, 05:12
a tricky equation

(1^m)+(2^m)=(3^m)
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Re: a tricky equation [#permalink] New post 10 Jun 2004, 05:15
stolyar wrote:
a tricky equation

(1^m)+(2^m)=(3^m)


really simple:

if m > 1 => 3^m > 2^m + 1^m.

if 0 < m < 1, then 3^m < 2^m + 1^m.

if m <= 0 => then 3^m = (1+2)^m < 1^m < 1^m + 2^m.

=> m = 1 is the only solution.
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 [#permalink] New post 10 Jun 2004, 06:09
yeah... not that tricky
agree with 1
  [#permalink] 10 Jun 2004, 06:09
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