# PARI code analyzing whether given integer is presentable as sum of two integer squares

Maximilian Hasler maximilian.hasler at gmail.com
Thu Nov 22 15:18:04 CET 2007

```Max,
by that token, can you explain (or at least give some comment on) the
very different results one gets for the divisors of a Gaussian integer
according to how it is written ?
I cannot find any rule...
Maximilian

(10:22) gp > divisors(1+0*I)
%87 = [1]

(10:24) gp > divisors(5+0*I)
%95 = [1, -I, 2 + I, 1 - 2*I, 1 + 2*I, 2 - I, 5*I, 5]
(10:24) gp > #%
%96 = 8
(10:24) gp > divisors(5*I)
%93 = [1, 2 + I, 1 + 2*I, 5*I]
(10:24) gp > #%
%94 = 4
(10:23) gp > divisors(5/I)
%91 = [1, -1, 2 + I, -2 - I, 1 + 2*I, -1 - 2*I, 5*I, -5*I]
(10:24) gp > #%
%92 = 8

(10:23) gp > divisors(4+0*I)
%88 = [1, -1, 1 + I, -1 - I, 2*I, -2*I, -2 + 2*I, 2 - 2*I, -4, 4]
(10:23) gp > divisors(4*I)
%89 = [1, -I, 1 + I, 1 - I, 2*I, 2, -2 + 2*I, 2 + 2*I, -4, 4*I]
(10:23) gp > divisors(4/I)
%90 = [1, I, 1 + I, -1 + I, 2*I, -2, -2 + 2*I, -2 - 2*I, -4, -4*I]

```