1 is definitely not a prime power. It's basically the same reason that 1 is not a prime.
Some reasons: (1) positive integers are uniqely products of prime powers (with 1 being the empty product!) Uniqueness would fail if 1 were allowed. (2) a positive integer n is a prime power iff nZ is a primary ideal of Z (that got you 2 marks in an exam I set this year), and the definition of primary ideal (as with prime ideal) explicitly requires the ideal to be proper. John On 29 August 2014 09:31, Jeroen Demeyer <jdeme...@cage.ugent.be> wrote: > Personally, I think "1" should not be considered a prime power, but Sage > thinks otherwise: > > sage: 1.is_prime_power() > True > > Of course, one could argue that 1 = p^0 for every prime p... > > Should this be changed, any opinions? > > -- > You received this message because you are subscribed to the Google Groups > "sage-devel" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to sage-devel+unsubscr...@googlegroups.com. > To post to this group, send email to sage-devel@googlegroups.com. > Visit this group at http://groups.google.com/group/sage-devel. > For more options, visit https://groups.google.com/d/optout. > -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
