MAPLE: Solve Equation with 3 unknowns in $\mathbb{Z}$

Question

I am trying to input in MAPLE

solve(23x+15y+18z = 11780, {x,y,z})

And it returns

{x=x, y = -23/15 x +2356/3 -6/5 z, z=z}

But I want it better to return something like

{x = 211 ,y = 223, z = 199}

How can I achieve to have the result in Relatives.

Thank you in advance

Answer 1

If "the smallest one" means the one that minimizes $x^2 + y^2 + z^2$, you could try

> extrema(x^2+y^2+z^2,{23*x+15*y+18*z=11780},{x,y,z},p);

$$\frac{69384200}{539}$$

> p;

$$ \left\{ \left\{ x={\frac{135470}{539}},y={\frac{88350}{539}},z={ \frac{106020}{539}} \right\} \right\} $$