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Re: function reduction
*To*: mathgroup at smc.vnet.net
*Subject*: [mg110757] Re: function reduction
*From*: Daniel Huber <dh at metrohm.com>
*Date*: Mon, 5 Jul 2010 06:01:29 -0400 (EDT)
*References*: <i0i1hr$hmf$1@smc.vnet.net>
On 01.07.2010 14:26, loke wrote:
> I am using wolfram alpha. When I enter
> solve( mod( 17 * y, 60 ) = 1 )
>
> It resolves it to a function
> y = 60 n+53 and n element Z
>
> How does it do it? I have tried this with other values, and it does it
> very well.
>
> Thanks
> Loke
>
Hi,
you may write your equation in form of a diophantine equation:
17 y==1+ 60 n
or
17 y + 60(-n) ==1
this then solves as:
60 == 60 (1) + 17 (0)
17 == 60 (0) + 17 (1) times (-3)
9 == 60 (1) + 17 (-3) times (-1)
8 == 60 (-1)+ 17(4) times (-1)
1 == 60 (2) + 17(-7)
this is one of many results. We get the others by adding zero(m from Z):
0 == 60 (17m)+17(-60m)
this gives:
1 == 60(2+ 17m)+ 17(-7-60m)
therefore we get for y:
y== -7-60m or equivalently: y= 53 + 60 n
Daniel
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