HP 50g Programming Competition: How Many Partitions of an Integer in 4 Squares

[Gerald H]

As is well-known, every integer can be represented as sum of max 4 squares

https://en.wikipedia.org/wiki/Lagrange%2...re_theorem

& that the number of such representations can be calculated as

https://en.wikipedia.org/wiki/Jacobi%27s...re_theorem

respecting order & sign.

The task is to write a User RPL programme to calculate the number of representations of any natural number exactly & swiftly.

Winner will be programme with lowest value of time*cuberoot(size).

I have a programme that processes 720^20 in 5.6 sec.