- #1
thomas430
- 17
- 0
Hi everyone :-)
at http://mathworld.wolfram.com/CarmichaelNumber.html it says that a Carmichael number is one which satisfies Fermat's little theorem:
[tex]a^{n-1} \equiv 1 mod (n)[/tex]
for every choice of a which is co-prime to n, with 1 < a < n.
Why is the domain 1 < a < n specified?
A maths book that I'm reading says "Can it happen that n is a pseudoprime to all possible bases a? The answer is yes and such numbers are called Carmichael numbers."
Does this mean that the set (1,n) exhausts all possible bases a?
Thanks :-)
Thomas.
at http://mathworld.wolfram.com/CarmichaelNumber.html it says that a Carmichael number is one which satisfies Fermat's little theorem:
[tex]a^{n-1} \equiv 1 mod (n)[/tex]
for every choice of a which is co-prime to n, with 1 < a < n.
Why is the domain 1 < a < n specified?
A maths book that I'm reading says "Can it happen that n is a pseudoprime to all possible bases a? The answer is yes and such numbers are called Carmichael numbers."
Does this mean that the set (1,n) exhausts all possible bases a?
Thanks :-)
Thomas.