Carmichael numbers in other bases

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Discussion Overview

The discussion centers on the behavior of Carmichael numbers when applying Fermat's Little Theorem in different bases, specifically questioning whether a Carmichael number returns 1 when using base 3.

Discussion Character

  • Technical explanation, Debate/contested

Main Points Raised

  • One participant asks if a Carmichael number returns 1 when using Fermat's Little Theorem with base 3.
  • Another participant asserts that it should be the same across bases, questioning why it would differ.
  • A third participant references a specific example involving the Carmichael number 561 and expresses confusion regarding a claim that it does not return 1 for bases other than 3, 11, and 17.
  • A later reply clarifies that the discussion pertains to the base of the exponent rather than the base of notation, suggesting it should still yield 1.

Areas of Agreement / Disagreement

Participants express differing views on whether Carmichael numbers consistently return 1 across all bases when applying Fermat's Little Theorem, indicating a lack of consensus on this matter.

Contextual Notes

The discussion involves assumptions about the behavior of Carmichael numbers and the specific conditions under which Fermat's Little Theorem applies, which may not be fully articulated or agreed upon.

?uestionable
Does anyone know if a Carmichael number returns 1 if you use Fermat's Little Theorem on it base 3?
 
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Yeah, it's the same. Why would it be different?
 
Carmichael numbers in different bases

Iwas at this site:

http://www.newnation.ca/sniffy/fermat.htm

and it had the example 561= 3x11x17
and stated that except for the bases 3, 11 and 17 A^560 = 1 (mod 561), its this statement that has me confused. I was under the impression that Carmichael numbers returned 1 in all bases.
 
Oh, base of the exponent, not the base of notation.
Should still be 1 though.
 

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