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#1 2009-12-28 04:50:25
- bobbym
- Administrator
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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.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#2 2009-12-28 06:15:15
- mathsyperson
- Moderator
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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
- Administrator
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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.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#4 2009-12-28 08:26:34
- JaneFairfax
- Legendary Member
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Re: Fumble and Botch strike again.
Last edited by JaneFairfax (2009-12-28 08:26:54)
#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.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#6 2009-12-29 03:56:35
- JaneFairfax
- Legendary Member
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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. 
#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.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.