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#1 2009-12-28 04:50:25
- bobbym
- Administrator
Online
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.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#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
Online
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.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#4 2009-12-28 08:26:34
- JaneFairfax
- Legendary Member
Offline
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
Online
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.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#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. 
#7 2009-12-29 17:49:13
- bobbym
- Administrator
Online
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.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.