Solving Diophantine equations using Julia

Hi, I am new with Julia and I was wondering how can I solve a system of diophantine equations adding conditions to some of the variables. For example, I would like to find integers x, y, p, h, r, t that solve the equations
eqn1: (t+8)(15)=(p-8)(r-15)
eqn2: 58(x-15)=(y+8)(r-15)
eqn3: (x+40)(h-80)=40(y-80)
Subject to the constraints
r>0 and p>0.
In Matlab I would use solve([eqn1,eq2,eq3,conditions],[variables]) using ‘integer’ at the begining.

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For individual solutions, this could be approached with JuMP and GLPK in combination.
Linear integer programming problems are discussed in the documentation of JuMP.


Have a look at this function and see if it solves your problem