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Re: Diophantic Equations with Constraints


Just a quick and dirty way to test if there is a possibility of a solution
(maybe not integer) might be something like this.   The solution is in the
range of 0-47, so we can quickly see that with 148, there are no solutions.
However, 14 is in the range, so there is a "chance" there might be integer
solutions.

In[1]:=
3*x + 2*y - z /.
{x -> Interval[{3, 8}],
 y -> Interval[{0, 12}],
 z -> Interval[{1, 9}]}

Out[1]=
Interval[{0, 47}]

In[2]:=
FindInstance[

{3*x + 2*y - z == 14,
3 <= x <= 8,
0 <= y <= 12,
1 <= z <= 9},
{x, y, z}, Integers, 100]


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