Exercise 4. This software finds the idempotents in* Z*_{n}[*i*] =
{*a+bi*| *a, b* belong
to *Z*_{n}} (Gaussian
integers modulo
*n* ). Run the software for* n*
= 4, 8, 16, and
32. Make a conjecture about the number of idempotents when *n =
2*^{k}. Run the
software for *n* = 13, 17, 29, and 37. What do these values
of*
n *have
in common? Make a conjecture about the number of idempotents for these
*n*. Run the software for* n = 7, 11, 19, 23, 31,* and 43.
What do these values
of *n* have in common? Make a conjecture about the number of
idempotents for
these *n*.