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

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SVP
Joined: 03 Feb 2003
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a tricky equation (1^m)+(2^m)=(3^m [#permalink]  10 Jun 2004, 04:12
a tricky equation

(1^m)+(2^m)=(3^m)
Manager
Joined: 07 May 2004
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Location: Ukraine, Russia(part-time)
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Re: a tricky equation [#permalink]  10 Jun 2004, 04:15
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.
SVP
Joined: 03 Feb 2003
Posts: 1607
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Kudos [?]: 87 [0], given: 0

yeah... not that tricky
agree with 1
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