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<DIV>Suppose we look at the primitive roots of primes. Which of these are sum free? (All are product free, except p=2.) Checking for p<100, I find that only 2, 3, 5, 7, and 13 are sum free. I doubt that there are any more, but I don't see any way to prove it.</DIV>
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<DIV>Franklin T. Adams-Watters<BR>16 W. Michigan Ave.<BR>Palatine, IL 60067<BR>847-776-7645</DIV>
<DIV> </DIV> <BR>-----Original Message-----<BR>From: Edwin Clark <eclark@math.usf.edu><BR>To: jens@voss-ahrensburg.de<BR>Cc: Sequence Fans <seqfan@ext.jussieu.fr><BR>Sent: Tue, 17 Jan 2006 15:40:42 -0500 (EST)<BR>Subject: Re: Numbers with anticlosed sets of non-squares<BR><BR>
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<DIV class=AOLPlainTextBody id=AOLMsgPart_0_0edeffac-eae1-4860-bd26-3d5046a6105d><PRE><TT>On Tue, 17 Jan 2006 <A href="mailto:jens%40voss-ahrensburg.de">jens@voss-ahrensburg.de</A> wrote:
> Let R be a ring. We will call a subset T of R *anticlosed* if for any
> elements t1 and t2 of T, neither the sum t1 + t2 nor the product t1 * t2
> lies in T.
I suggest that you call such a subset "sum and product free".</TT></PRE></DIV></DIV></DIV>
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