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June 7th, 2013, 09:41 PM   #21
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Re: A new approach to Fermat's last theorem

Quote:
Originally Posted by McPogor
Quote:
First case of Fermat's last theorem
From Wikipedia, the free encyclopedia
The first case of Fermat's last theorem says that for three integers x, y and z and a prime number p, where p does not divide the product xyz, there are no solutions to the equation
My question is whether and are equivalent equations.
It is well known and can be easily proved that to have solution the latter requires XYZ to be divisible by N.
Then the inverse statement must be true as well:

If coprime with then has no solution.

It is an equivalent of this elaborated proof, isn't it.
If we assume there are integers solutions,then the two equations are not equivalent,as the accepts (actually needs) negative solutions,while the other one does not.But if we suppose or prove the lack of integer solutions, then the two are equivalent
I'm eager to see the easy proof you mentioned.Ceck this http://en.wikipedia.org/wiki/First_case ... st_theorem
For the case,see my may 31 12:23 remark
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June 8th, 2013, 01:36 AM   #22
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numbers

The smallest value of n,for which 2n +1 is not a prime number is...................................
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June 8th, 2013, 03:46 PM   #23
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Re: numbers

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Originally Posted by sanjay_jena13
The smallest value of n,for which 2n +1 is not a prime number is...................................
Ooooh! I know! 4!

Why?
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June 8th, 2013, 06:25 PM   #24
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Re: numbers

Quote:
Originally Posted by johnr
Ooooh! I know! 4!

Why?
n=0

If we do not consider prime number the "1"

Regards.
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June 8th, 2013, 11:39 PM   #25
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Re: A new approach to Fermat's last theorem

Poor FLT
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June 9th, 2013, 02:17 AM   #26
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Re: A new approach to Fermat's last theorem

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Originally Posted by bruno59
Poor FLT
You have reason, I sit it.
I ask him to excuse myself.

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June 9th, 2013, 05:00 AM   #27
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Re: numbers

Quote:
Originally Posted by mente oscura
Quote:
Originally Posted by johnr
Ooooh! I know! 4!

Why?
n=0

If we do not consider prime number the "1"

Regards.
Zzzzzzziinnggg! Point taken!
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June 11th, 2013, 02:38 PM   #28
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Re: A new approach to Fermat's last theorem

Quote:
For the case,see my may 31 12:23 remark
LET ME SEE IF I GET THE POINT
IF N DIVIDES ONE OF X,Y,Z, SAY Y (b=0), THEN FROM WE GET N|a
SO a=0, ABSURD
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June 11th, 2013, 10:29 PM   #29
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Re: A new approach to Fermat's last theorem

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Originally Posted by akenaton
LET ME SEE IF I GET THE POINT
IF N DIVIDES ONE OF X,Y,Z, SAY Y (b=0), THEN FROM WE GET N|a
SO a=0, ABSURD
That's right
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June 14th, 2013, 08:07 AM   #30
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Re: A new approach to Fermat's last theorem

Quote:
Originally Posted by bruno59
]
Step 1. Basic relations between X,Y,Z,N
Let

We first show that

Suppose this was'nt true.Then there would be a prime Q common in these two numbers:

and if

and as Q is a prime,we get j=Q and so

but since

we conclude that

which is false,because X and Y are coprimes.So:

and from (1) we see that

is all "hidden" in N:

and as N is a prime:

which is false.Therefore:

and since:

i am just posing doubt don't misunderstand...
is the last equation correct...
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