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Topic: number with ....
Replies: 20   Last Post: Jan 5, 2007 8:16 PM

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Ara M Jamboulian

Posts: 65
Registered: 12/6/04
Re: number with ....
Posted: Jan 5, 2007 6:25 AM
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> Hello sir~
>
> x + 6xy - y = 1.
>
> (x and y are positive integer).
>
> ----------------------------------
> I think....
> This equation does not exist a solution.
> right ?
>
> and then,
> How can you show that this does not have a solution ?
>
> so, I need your advice.
>
>


>> Conclusion:
>> the equation x + 6xy - y = a in x,y with x,y positive integer ; a given
>> positive integer has an unique solution x = 1 and y = (a-1)/5 iff a = 1
>> mod 5. Otherwise it has no solution.


>>Yes, nice generalization.
>>Thank you very much.


there is something wrong with this generalization.
e.g.
x + 6 x y - y = 20 has solutions (x=3, y=1)



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