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

单词

Bauer's Identical Congruence

释义

Bauer's Identical Congruence

Let denote the set of the numbers less than and Relatively Prime to , where is theTotient Function. Define

(1)

A theorem of Lagrange states that

(2)

This can be generalized as follows. Let

be an Odd Prime Divisor of

and

thehighest Power which divides

, then

(3)

and, in particular,

(4)

Furthermore, if

is Even and

is the highest Power of 2 that divides

, then

(5)

and, in particular,

(6)

See also Leudesdorf Theorem

References

Hardy, G. H. and Wright, E. M. ``Bauer's Identical Congruence.'' §8.5 in An Introduction to the Theory of Numbers, 5th ed. Oxford, England: Clarendon Press, pp. 98-100, 1979.

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