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Diophantic linear Equations

vlehner
14-Alexandrite

Diophantic linear Equations

Good morning to all,

currently i'm dealing with the theory of numbers where i have to find the solutions of a linear diophantic equation in common.

Is there any way in MP4 to call up a function for this problem, does there exist an implemented function in Prime for this?

Thanks in Advance

Volker

Volker
6 REPLIES 6

The simplest linear Diophantine equation takes the form

ax + by = c,

where a, b and c are given integers, x, y — unknowns.

The solutions are completely described by the following theorem: This Diophantine equation has a solution (where x and y are integers) if and only if c is a multiple of the greatest common divisor of a and b. Moreover, if (x, y) is a solution, then the other solutions have the form (x + kv, y - ku), where k is an arbitrary integer, and u and v are the quotients of a and b (respectively) by the greatest common divisor of a and b.To find the solution one can use Extended Euclidean algorithm (except for a = b = 0 where either there are unlimited number of solutions or none).

 

Mathcad has a gcd function that will determine greatest common divisor.  gcd(a,b)

You can determine if c is a multiple by testing the mod function for zero return. mod(c,gcd(a,b))=0 is pass

You could program to search for them.

 

 

 

vlehner
14-Alexandrite
(To:terryhendicott)

So in summary i have to programm a routine because of the fact that there is no special function in MP4 for this.

THX anyway.

 

Volker
ViktorKorobov
14-Alexandrite
(To:vlehner)


@vlehner wrote:

So in summary i have to programm a routine because of the fact that there is no special function in MP4 for this.

THX anyway.

 


File in Mathcad Prime 3.1 format attached.

Diophantine.png

 

Viktor

спасибо виктор,

In Mathacd 11:

LM_20170927_IntegerSolve.png

 

Luc

vlehner
14-Alexandrite
(To:LucMeekes)

Thanks Victor and Werner.

I tryed to run isolve() in MC15, and it will not work. Is it possible to run this function in MC15?

I have not the good old MC11.

 

Volker
ViktorKorobov
14-Alexandrite
(To:vlehner)

No, isolve not work in MC15. It was an undocumented symbolics command in Mathcad 11.

Viktor
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