Well, I have the following code: PowersRepresentations[1000, 5, 2]
and this code gives me 145 solutions. But I want to filter the solutions, in the problem that I am working on the solution involving a 0 or a solution with two or more of the same numbers is not what I am looking for.
Question: How can I filter in the solutions found by the code PowersRepresentations[1000, 5, 2]
that only gives unique* solutions not involving a zero?
*: This means that when a given solution looks like: {{a1,a2,a3,a4,a5},{b1,b2,b3,b4,b5},...}
I am looking for the ones where:
- $$a_1\ne a_2\ne a_3\ne a_4\ne a_5\tag1$$ For all $a_n$ and $b_n$ etc., so $a_n\ne a_{n+1}$ and $b_n\ne b_{n+1}$ etc.
- $$\forall a_n>0\space\wedge\space\forall b_n>0...\text{etc}.\tag2$$