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