“Carmichael Function”的概念、定义、习题解题方法及翻译-数学辞典

单词

Carmichael Function

释义

Carmichael Function

is the smallest integer such that for all Relatively Prime to . It can bedefined recursively by

Some special values are

for

, and

for

an Odd Prime and

. The Order of

(mod

) is at most

(Ribenboim 1989). The values of

for the first few

are 1, 1, 2, 2, 4, 2, 6, 2, 6, 4, 10, 2, 12, ...(Sloane's A002322).

See also Modulo Multiplication Group

References

Ribenboim, P. The Book of Prime Number Records, 2nd ed. New York: Springer-Verlag, p. 27, 1989.

Riesel, H. ``Carmichael's Function.'' Prime Numbers and Computer Methods for Factorization, 2nd ed. Boston, MA: Birkhäuser, pp. 273-275, 1994.

Sloane, N. J. A. SequenceA002322/M0298in ``An On-Line Version of the Encyclopedia of Integer Sequences.''http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S.The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.

Vardi, I. Computational Recreations in Mathematica. Redwood City, CA: Addison-Wesley, p. 226, 1991.

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