Number Theory(congruance)
If $x^3+y^3=z^3$ Show that one of the three must be a multiple of 7
Last edited by Hasib on Fri Dec 10, 2010 10:10 pm, edited 5 times in total.
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Re: Number Theory(congruance)
Hasib, why don't you consider using LaTeX? Now, you can write equations without knowing it!
viewtopic.php?f=9&t=54&p=175#p175
viewtopic.php?f=9&t=54&p=175#p175
"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin
Please install LaTeX fonts in your PC for better looking equations,
learn how to write equations, and don't forget to read Forum Guide and Rules.
Please install LaTeX fonts in your PC for better looking equations,
learn how to write equations, and don't forget to read Forum Guide and Rules.
Re: Number Theory(congruance)
Why my code doesnt working?
A man is not finished when he's defeated, he's finished when he quits.
Re: Number Theory(congruance)
Hasib, I can see your equation just fine. Please clean the cache of your browser and try again. If you are using firefox then go to Tools>Options>Advanced then click "Clear Now".
Let me know if that solves your problem. Thanks.
Let me know if that solves your problem. Thanks.
"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin
Please install LaTeX fonts in your PC for better looking equations,
learn how to write equations, and don't forget to read Forum Guide and Rules.
Please install LaTeX fonts in your PC for better looking equations,
learn how to write equations, and don't forget to read Forum Guide and Rules.
Re: Number Theory(congruance)
We use the fact $a^3\equiv 0,\pm 1\ (mod\ 7)$
If none of $x,y,z$ divisible by $7,$then we have:
$x^3+y^3\equiv \pm(1+1)\equiv \pm 2\ (mod\ 7)$ but $z^3$ is not $\equiv \pm 2\ (mod\ 7)$.Contradiction
If none of $x,y,z$ divisible by $7,$then we have:
$x^3+y^3\equiv \pm(1+1)\equiv \pm 2\ (mod\ 7)$ but $z^3$ is not $\equiv \pm 2\ (mod\ 7)$.Contradiction
One one thing is neutral in the universe, that is $0$.
Re: Number Theory(congruance)
ThanQ Moon vaia /clubsuit
A man is not finished when he's defeated, he's finished when he quits.
Re: Number Theory(congruance)
Dear Hasib,are you considering $x^3+y^3=z^3$?
Re: Number Theory(congruance)
@nmmahi: yeah \[\clubsuit^{\clubsuit\clubsuit}\clubsuit\]
A man is not finished when he's defeated, he's finished when he quits.
Re: Number Theory(congruance)
@Masum vai: i think, this problem is very interesting. Cause, with the Fermat's last theorem we know there is no positive solution of this form \[a^n+b^n=c^n\] whence \[n\ge 3\]
so, how we prove this one? I think it's a great DOSS! I take the problem from The Art and Craft of Problem Solving.\[\clubsuit^\clubsuit\clubsuit\]
so, how we prove this one? I think it's a great DOSS! I take the problem from The Art and Craft of Problem Solving.\[\clubsuit^\clubsuit\clubsuit\]
A man is not finished when he's defeated, he's finished when he quits.
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Re: Number Theory(congruance)
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