Sum of many rational squares to integer. I would like to know if there is already a general method to solve it.

Feb 2020
5
1
Brazil
Hello people, can somebody help me?

Some time ago I got to solve this problem, but I don´t know whether it is already solved. I read Dickson, but didn't find something general for many rational squares. The book just talks about two, three or four rational squares sum, but not unlimited number of them.

I am thinking publish the algorithm in some journal (I don´t know where), but first need to know whether it is interesting in some way.

Some examples:

find Xi such

x1^2 + x2^2 + x3^2 + x4^2 = 7.C^2

solution

47^2 + 38^2 + 37^2 + 75^2 = 7.39^2

another example

1.x1^2 + 2.x2^2 + 3.x3^2 + 4.x4^3 + 5.x5^2 = 6.C^2

solution

1.77^2 + 2.61^2 + 3.67^2 + 4.(-2)^2 + 5.(-4)^2 = 6.67^2

Thanks in advance

Miguel Velilla