“Giuga's Conjecture”的概念、定义、习题解题方法及翻译-数学辞典

单词

Giuga's Conjecture

释义

Giuga's Conjecture

If and

necessarily a Prime? In other words, defining

does there exist a Composite

such that

? It is known that

Iff for eachprime divisor

and

(Giuga 1950, Borwein et al. 1996); therefore, any counterexample mustbe Squarefree. A composite Integer

satisfies

Iff it is both a CarmichaelNumber and a Giuga Number. Giuga showed that there are no exceptions to the conjecture up to

. This waslater improved to

(Bedocchi 1985) and

(Borwein et al. 1996).

See also Argoh's Conjecture

References

Bedocchi, E. ``The Ring and the Euclidean Algorithm.'' Manuscripta Math. 53, 199-216, 1985.

Borwein, D.; Borwein, J. M.; Borwein, P. B.; and Girgensohn, R. ``Giuga's Conjecture on Primality.'' Amer. Math. Monthly 103, 40-50, 1996.

Giuga, G. ``Su una presumibile propertietà caratteristica dei numeri primi.'' Ist. Lombardo Sci. Lett. Rend. A 83, 511-528, 1950.

Ribenboim, P. The Book of Prime Number Records, 2nd ed. New York: Springer-Verlag, pp. 20-21, 1989.

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