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#1 2007-08-06 18:55:40

haruka-san
Member
Registered: 2006-11-08
Posts: 205

Number Theory

can someone please help me with these problems?

Solve for the values of x, y, and z.

1. 12x + 15y - 17z = 1

uhmm this is somewhat related with Greatest common divisor and Euclidean Algorithm.. and our professor says that the Diophantine equation can also be used.. smile

please give me a complete solution.
I need at least 10 values of x, y and z.

i hope someone can help me...

thanks in advance! smile


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#2 2007-08-06 19:48:03

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,905

Re: Number Theory

OK.
First, assuming you want only integer answers...
There are many ways, but I use this:
(it's long...)


,
so
should be integer. Call it w:


, so
should be integer, name it q:

, and (q-1)/2 should be integer.



Now:


, so
must be integer - m:


Now, returninig up:

and upper:

So solution is:
for r,m integers.
But there are other ways for expressing this, as:
ect.


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#3 2007-08-13 21:29:36

haruka-san
Member
Registered: 2006-11-08
Posts: 205

Re: Number Theory

to krassi_holmz,

i just wanted to say "thank you" for answering this problem and giving such a complete solution.
you really helped me a lot!!!  thanks thanks thanks thanks.. smile
a lot of thanks from me! smile

haruka-san


Don’t compare your life to others. You have no idea what their journey is all about. ^_^

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