# Right solver for JuMP to find every solution of a linear system of equations with integer solutions

**URL:** <https://discourse.julialang.org/t/right-solver-for-jump-to-find-every-solution-of-a-linear-system-of-equations-with-integer-solutions/44709>\
**Category:** Optimization (Mathematical)\
**Tags:** question, jump\
**Created:** [August 10, 2020, 9:44pm UTC](https://discourse.julialang.org/t/right-solver-for-jump-to-find-every-solution-of-a-linear-system-of-equations-with-integer-solutions/44709 "2020-08-10T21:44:52Z")\
**Posts on this page:** 1\
**Showing post:** 14

<div class="post-metadata">

**Author:** ![damaro](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/damaro/32/17002_2.png) [@damaro](https://discourse.julialang.org/u/damaro)\
**Post date:** [August 11, 2020, 7:24pm UTC](https://discourse.julialang.org/t/right-solver-for-jump-to-find-every-solution-of-a-linear-system-of-equations-with-integer-solutions/44709/14 "2020-08-11T19:24:26Z")

</div>

There are the 24 solutions (returned by Mathematica):

```julia
0,0,0,0,0,0,1,1,1,2,0,0,1,0,0,0
0,0,0,0,0,0,1,1,2,1,0,0,0,1,0,0
0,0,0,0,0,1,0,1,1,1,1,0,1,0,0,0
0,0,0,0,0,1,0,1,2,0,1,0,0,1,0,0
0,0,0,0,0,1,0,1,2,1,0,0,0,0,1,0
0,0,0,0,0,1,1,0,1,1,0,1,1,0,0,0
0,0,0,0,0,1,1,0,2,0,0,1,0,1,0,0
0,0,0,0,0,1,1,0,2,1,0,0,0,0,0,1
0,0,0,0,0,2,0,0,1,0,1,1,1,0,0,0
0,0,0,0,0,2,0,0,2,0,0,1,0,0,1,0
0,0,0,0,0,2,0,0,2,0,1,0,0,0,0,1
0,0,0,0,1,0,0,1,0,2,1,0,1,0,0,0
0,0,0,0,1,0,0,1,1,1,1,0,0,1,0,0
0,0,0,0,1,0,0,1,1,2,0,0,0,0,1,0
0,0,0,0,1,0,1,0,0,2,0,1,1,0,0,0
0,0,0,0,1,0,1,0,1,1,0,1,0,1,0,0
0,0,0,0,1,0,1,0,1,2,0,0,0,0,0,1
0,0,0,0,1,1,0,0,0,1,1,1,1,0,0,0
0,0,0,0,1,1,0,0,1,0,1,1,0,1,0,0
0,0,0,0,1,1,0,0,1,1,0,1,0,0,1,0
0,0,0,0,1,1,0,0,1,1,1,0,0,0,0,1
0,0,0,0,2,0,0,0,0,1,1,1,0,1,0,0
0,0,0,0,2,0,0,0,0,2,0,1,0,0,1,0
0,0,0,0,2,0,0,0,0,2,1,0,0,0,0,1

```

I tried checking both solutions (yours and Mathematica) using `sort` with no avail. I’ll send the results soon, but I’m confident both are equal.

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