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 Post subject: One TaskPosted: Tue, 1 Nov 2011 20:33:31 UTC

Joined: Tue, 1 Nov 2011 00:12:51 UTC
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a, k are natural numbers
I must find all a

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 Post subject: Re: One TaskPosted: Tue, 1 Nov 2011 20:48:24 UTC
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Patron wrote:

a, k are natural numbers
I must find all a

multiply both sides by k-1 (justify why this is OK), solve linear equation.

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 Post subject: Re: One TaskPosted: Tue, 1 Nov 2011 21:30:07 UTC
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solutions infinite (except a<>62).

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 Post subject: Re: One TaskPosted: Tue, 1 Nov 2011 21:33:33 UTC

Joined: Tue, 1 Nov 2011 00:12:51 UTC
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I knows results. a=63, 65, 69, 71 ,83, 125, but my system is very complicated.

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 Post subject: Re: One TaskPosted: Tue, 1 Nov 2011 22:43:21 UTC
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Denis wrote:
solutions infinite (except a<>62).

What? For fixed and (for which the right side is not defined, so this is not well-defined) we can see that , which has no solution for as you note, but otherwise, it's easy to see there is a unique solutions of , which is uniquely determined by . . .

I mean in general this should be obvious because the given function is a MÃ¶bius transform, which is an analytic isomorphism of the Riemann sphere, so if you consider the punctured sphere, you need to only punch out the preimage of infinity, in this case and you're fine, and you still get a 1-1 function descending from the original by restriction.

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 Post subject: Re: One TaskPosted: Wed, 2 Nov 2011 02:40:25 UTC
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Hello, Patron!

Quote:

We have: .

Since is a natural number, must be a factor of 63.

And we have six solutions: .

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 Post subject: Re: One TaskPosted: Wed, 2 Nov 2011 04:36:54 UTC
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Ok ok .... missed the word "natural" ...

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 Post subject: Re: One TaskPosted: Wed, 2 Nov 2011 04:37:37 UTC
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Denis wrote:
Ok ok .... missed the word "natural" ...

As did I, but I'm still not sure how you got infinitely many solutions?

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