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

单词

Binomial Number

释义

Binomial Number

A number of the form , where , and are Integers. They can be factored algebraically

(1)

(2)

(3)

In 1770, Euler

proved that if

, then every Factor of

(4)

is either 2 or of the form

. If

and

are Primes, then

(5)

is Divisible by every Prime Factor of

not dividing

See also Cunningham Number, Fermat Number, Mersenne Number, Riesel Number, Sierpinski Numberof the Second Kind

References

Guy, R. K. ``When Does Divide .'' §B47 in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, p. 102, 1994.

Qi, S and Ming-Zhi, Z. ``Pairs where Divides for All .'' Proc. Amer. Math. Soc. 93, 218-220, 1985.

Schinzel, A. ``On Primitive Prime Factors of .'' Proc. Cambridge Phil. Soc. 58, 555-562, 1962.

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