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#1 2009-12-28 04:50:25

bobbym
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Fumble and Botch strike again.

Hi;

It is well known that:



Prove that:



Has no solution in integers:

Proof:

8x^2 is congruent to {0,2,5,8} mod 9

270y^4 is congruent to 0 mod 9

So 8x^2 + 270y^4 is congruent to {0,2,5,8} mod 9

While 210 is congruent to 3 mod 9:

So 8x^2 + 270y^4 = 210 has no solutions in integers.

Total garbage! What is wrong with this?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#2 2009-12-28 06:15:15

mathsyperson
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Re: Fumble and Botch strike again.

As far as I can tell the proof is sound. The statement is certainly true, and here's a simpler way of showing it:

If y is a non-zero integer, then y^4 is a positive integer.
Also, x^2 is non-negative for all integers x, and so we must have 270y^4 = 0 if there is any chance of solving the equation.

However, we are then left with x^2 = 210/8, which has no integer solutions.


Why did the vector cross the road?
It wanted to be normal.
 

#3 2009-12-28 06:23:25

bobbym
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Re: Fumble and Botch strike again.

Hi;

Confucius wrote:

Do not use a cannon to kill a mosquito

That is exactly what is wrong with it. Lot of typing no thinking.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#4 2009-12-28 08:26:34

JaneFairfax
Legendary Member

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Re: Fumble and Botch strike again.

and
and so for the equation to have any solution, we must have
. That means
, which means
and so
. Then the LHS would be divisible by 9 whereas the RHS isnt.

Last edited by JaneFairfax (2009-12-28 08:26:54)


Q: Who wrote the novels Mrs Dalloway and To the Lighthouse?

A: Click here for answer.
 

#5 2009-12-28 11:52:17

bobbym
Administrator

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Re: Fumble and Botch strike again.

Hi Jane;

Yes, the poster missed that too. He seems to love mods, uses them to prove or disprove everything.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#6 2009-12-29 03:56:35

JaneFairfax
Legendary Member

Offline

Re: Fumble and Botch strike again.

There is nothing wrong with mods; I use them a lot too. But I also like to keep my mind open for simple solutions, if they exist. smile


Q: Who wrote the novels Mrs Dalloway and To the Lighthouse?

A: Click here for answer.
 

#7 2009-12-29 17:49:13

bobbym
Administrator

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Re: Fumble and Botch strike again.

Hi Jane;

If the simple solution is the only one available, then I am sure you will use it. No insult intended but my assessment of you is that your artistic side, dominates.

In case I don't see you, have a happy New Year!


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

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