#10343: primitive_root(ZZ) ArithmeticError for (+-)2^i for i >= 3
-----------------------------+----------------------------------------------
Reporter: donmorrison | Owner: was
Type: defect | Status: new
Priority: major | Milestone: sage-4.6.1
Component: number theory | Keywords: primitive root PARI
Author: | Upstream: Not yet reported upstream; Will do
shortly.
Reviewer: | Merged:
Work_issues: |
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Gauss' Table of Primitive Roots and Indices gives primitive root g=5 as an
example primitive root, for p!^i == 16 == 2!^4
Looks like a PARI bug:
sage: primitive_root(16)
---------------------------------------------------------------------------
!ArithmeticError Traceback (most recent call
last)
/home/donmorrison/sage46fromsrc/sage/<ipython console> in <module>()
/home/donmorrison/sage46fromsrc/sage/local/lib/python2.6/site-
packages/sage/rings/arith.pyc in primitive_root(n)
3359 return ZZ(pari(ZZ(n)).znprimroot())
3360 except !RuntimeError:
-> 3361 raise !ArithmeticError, "There is no primitive root modulo
n"
3362
3363 def nth_prime(n):
!ArithmeticError: There is no primitive root modulo n
sage:
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10343>
Sage <http://www.sagemath.org>
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