Author Topic: a^2 + b^2 = c^2  (Read 6179 times)

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Offline Genesis

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a^2 + b^2 = c^2
« on: June 20, 2006, 10:15:27 pm »
Prove or disprove that, if n be a number greater than 2, there are no whole numbers such that a^n +b^n =c^n

a, b, and c have to be positive and n > 2

Enjoy! I don't think even Oviraptor can solve this one!

PM me if you think you have it, and feel free to post comments and hints here.
« Last Edit: June 20, 2006, 11:34:47 pm by Genesis »



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Offline Kratok

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Re: a2 + b2 = c2
« Reply #1 on: June 20, 2006, 10:18:10 pm »
I
B
A
Y

Offline Clayface

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Re: a2 + b2 = c2
« Reply #2 on: June 20, 2006, 11:13:07 pm »
a2 + b2 = c2


 ???
do you mean a^2+b^2=c^2
or 2a + 2b = 2c
im confused

Offline Genesis

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Re: a2 + b2 = c2
« Reply #3 on: June 20, 2006, 11:13:42 pm »
The first one.

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Offline Clayface

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Re: a2 + b2 = c2
« Reply #4 on: June 20, 2006, 11:14:29 pm »
and do you want us to write it out as a proof?


Offline Genesis

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Re: a^2 + b^2 = c^2
« Reply #5 on: June 20, 2006, 11:15:41 pm »
Explaining your conclusion is the entire point.

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Offline Clayface

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Re: a^2 + b^2 = c^2
« Reply #6 on: June 20, 2006, 11:20:50 pm »
well that only works with multiples of 3,4,and 5 plugged into a,b,and c respectably,

so
3^2+4^2=5^2
6^2+8^2=10^2
. . . .
. . . .
45^2+60^2=75^2
ect,

if you try plugging in any numbers that dont follow that pattern, it wont work.

Offline Daxx

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Re: a^2 + b^2 = c^2
« Reply #7 on: June 20, 2006, 11:23:12 pm »
Let a=c and b=0 (alternatively, let a=0 and b=c).

The equation now holds for all non-zero values of n.
« Last Edit: June 20, 2006, 11:31:29 pm by Daxx »

Offline Genesis

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Re: a^2 + b^2 = c^2
« Reply #8 on: June 20, 2006, 11:33:49 pm »
Sorry, forgot to put that a, b, and c have to be positive and n > 2 I'll add that now. Sorry I forgot that but its 2:30 for me right now.

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Offline Clayface

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Re: a^2 + b^2 = c^2
« Reply #9 on: June 20, 2006, 11:42:29 pm »
that would be very very easy to prove wrong.

Offline Genesis

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Re: a^2 + b^2 = c^2
« Reply #10 on: June 20, 2006, 11:43:22 pm »
Do it.

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Offline Quantum Burrito

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Re: a^2 + b^2 = c^2
« Reply #11 on: June 20, 2006, 11:44:31 pm »
that would be very very easy to prove wrong.

*uncontrolable laughter*

*snort* where do they come from?
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tl;dr. But with all those shiny symbols and numbers it's probably awsome.

Offline Genesis

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Re: a^2 + b^2 = c^2
« Reply #12 on: June 20, 2006, 11:46:33 pm »
Wait do you mean what I forgot to add, **** I KNEW that would happen! WHY does nobody believe me when I forget something?  :'(

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Offline Clayface

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Re: a^2 + b^2 = c^2
« Reply #13 on: June 20, 2006, 11:51:52 pm »
well one way to prove it wrong would be to sell the values of a, b, and c all to 3

3^2+3^2=3^2
9+9=9
18=9

. . . .
WRONG

Offline Daxx

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Re: a^2 + b^2 = c^2
« Reply #14 on: June 20, 2006, 11:53:39 pm »
well one way to prove it wrong would be to sell the values of a, b, and c all to 3

3^2+3^2=3^2
9+9=9
18=9

. . . .
WRONG

Uh, no. That's not a proof that there are no numbers which satisfy the equation. It's like saying that there are no numbers which satisfy x+1=2 by using x=3 as a demonstration.