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Revision History for A005935

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Showing entries 1-10 | older changes

A005935

Pseudoprimes to base 3.
(history; published version)

#70 by Charles R Greathouse IV at Wed Feb 09 01:03:11 EST 2022

STATUS

editing

approved

#69 by Charles R Greathouse IV at Wed Feb 09 01:03:06 EST 2022

CROSSREFS

Subsequence of A122780.

Cf. A005382, A122780.

STATUS

approved

editing

#68 by N. J. A. Sloane at Thu Apr 01 15:17:36 EDT 2021

STATUS

editing

approved

#67 by N. J. A. Sloane at Thu Apr 01 15:17:28 EDT 2021

COMMENTS

Theorem (R. Steuerwald, 1948): if n is a pseudoprime to base b and gcd(n,b-1)=1, then (b^n-1)/(b-1) is a pseudoprime to base b. Especially, In particular, if n is an odd pseudoprime to base 3, then (3^n-1)/2 is a pseudoprime to base 3. - Thomas Ordowski, Apr 06 2016

STATUS

proposed

editing

Discussion

Thu Apr 01

15:17

N. J. A. Sloane: edited

#66 by Amiram Eldar at Wed Mar 17 08:20:43 EDT 2021

STATUS

editing

proposed

#65 by Amiram Eldar at Wed Mar 17 08:20:25 EDT 2021

REFERENCES

R. Steuerwald, Über die Kongruenz a^(n-1) == 1 (mod n). Sitzungsber. math.-naturw. Kl. Bayer. Akad. Wiss. München, 1948, pp. 69-70.

LINKS

Rudolf Steuerwald, <a href="https://www.zobodat.at/pdf/Sitz-Ber-Akad-Muenchen-math-Kl_1948_0069-0070.pdf">Über die Kongruenz a^(n-1) == 1 (mod n)</a>, Sitzungsber. math.-naturw. Kl. Bayer. Akad. Wiss. München, 1948, pp. 69-70.

STATUS

proposed

editing

#64 by Thomas Ordowski at Tue Feb 23 06:23:17 EST 2021

STATUS

editing

proposed

Discussion

Mon Mar 15

10:58

Thomas Ordowski: Let m = (b^n-1)/(b-1). Theorem: if m == 1 (mod n), then b^(m-1) == 1 (mod m). Conjecture: if b^(m-1) == 1 (mod m), then m == 1 (mod n).

#63 by Thomas Ordowski at Tue Feb 23 06:22:16 EST 2021

COMMENTS

Steuerwald's theorem can be strengthened by weakening his assumption as follows: if n is a weak pseudoprime to base b and gcd(n,b-1)=1, then ... - Thomas Ordowski, Feb 23 2021

#62 by Thomas Ordowski at Tue Feb 23 06:19:38 EST 2021

COMMENTS

Steuerwald's theorem can be strengthened by weakening the his assumption as follows: if n is a weak pseudoprime to base b ... - Thomas Ordowski, Feb 23 2021

#61 by Thomas Ordowski at Tue Feb 23 06:13:48 EST 2021

COMMENTS

Steuerwald's theorem can be strengthened by weakening the assumption: if n is a weak pseudoprime to base b ... - Thomas Ordowski, Feb 23 2021

STATUS

proposed

editing