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Hi,
can anyone give me a hint how to prove that the following equation can not be solved with integers for x and y?
x³+y³=4(x²y+xy²+1)
thanks
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"Want proof? Well, YOU try solving it!"
I have nothing of value to add, just my lame sense of humor.
El que pega primero pega dos veces.
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diophantine equations has something about integer answers.
igloo myrtilles fourmis
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well theres the sum and difference of two cubes identity, though I don't really see how that would help you here.
A logarithm is just a misspelled algorithm.
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Thanks, Diophantine Equations helped me, cause they led me to Fermat's Theorem(Generalized Equation: x^n+y^n=c*z^n)
x³+y³=4(x²y+xy²+1) |*2
2x³+2y³= (x²y+xy²+1)*8[or: 2^3]
Therefore no integer-solutions are possible.
Last edited by mling (2006-03-01 19:31:08)
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Here's my proof:
Let A is the equation:
IPBLE: Increasing Performance By Lowering Expectations.
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krassi, It appears you've been learning a lot of new stuff lately.
That's terrific.
What does the "|" symbol mean in above work?
igloo myrtilles fourmis
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| means divides.
2 | 4
3 | 30
The equivalent of:
x | y
is:
y = xk, where k is some integer
That is, y is a multiple of x (and k).
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."
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so x | y means y mod x = 0 , Thanks.
igloo myrtilles fourmis
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yes, but the normal way to write that is:
y = 0 mod x.
Don't get me wrong, your way is perfectly fine too. I guess I'm just used to seeing the mod and 0 on the right.
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."
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No. The normal way is with 3 lines:
x ≡ 0 (mod y)
IPBLE: Increasing Performance By Lowering Expectations.
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My proof makes me think that the Fetmat's generalized equation is true.
IPBLE: Increasing Performance By Lowering Expectations.
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