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- Newsgroups: sci.math
- Path: sparky!uunet!zaphod.mps.ohio-state.edu!sdd.hp.com!think.com!linus!linus.mitre.org!fatima!bs
- From: bs@fatima.mitre.org (Robert D. Silverman)
- Subject: Re: puzzling squares
- Message-ID: <1992Oct8.011507.29363@linus.mitre.org>
- Sender: news@linus.mitre.org (News Service)
- Nntp-Posting-Host: fatima.mitre.org
- Organization: Research Computer Facility, MITRE Corporation, Bedford, MA
- References: <UDQ750@gwdu03.gwdg.de>
- Date: Thu, 8 Oct 1992 01:15:07 GMT
- Lines: 18
-
- In article <UDQ750@gwdu03.gwdg.de> moeller@gwdgv1.gwdg.de writes:
-
- stuff deleted....
-
- :To prove that this is indeed the smallest such number,
- :one had to show that (10^(2*k) + 1) is square-free, for (2*k) < 136.
- :Does the current state of the "art of factorization" allow for this check?
-
- All number of the form 10^n + 1 have been factored for n = 1 to 148.
- [10^149+1 is the first such that has not been completely factored].
- 10^{2k} + 1 is indeed squarefree for 2k < 136. For 2k=136, it is
- divisible by 17^2.
-
- --
- Bob Silverman
- These are my opinions and not MITRE's.
- Mitre Corporation, Bedford, MA 01730
- "You can lead a horse's ass to knowledge, but you can't make him think"
-