BranchesHistoryHelpLogin
Welcome guest
You're not logged in.
251 users online, thereof 0 logged in

Corollary: Sums, Products, and Powers Of Congruences

Let $m > 0$ be a positive integer and let $a_1,\ldots,a_r$ be integers. Then the sum and the product of the congruences $a_i(m)$, $i=1,\ldots,r$ are defined by

$$\sum_{i=1}^ra_i(m):=\left(\sum_{i=1}^ra_i\right)(m),$$

$$\prod_{i=1}^ra_i(m):=\left(\prod_{i=1}^ra_i\right)(m).$$

For any integer $a$, we set the power of the congruence $a(m)$ by

$$(a(m))^r:=(a^r)(m).$$

| | | | | created: 2019-04-13 08:05:23 | modified: 2019-04-13 08:11:24 | by: bookofproofs | references: [1272], [8152]

1.Proof: (related to "Sums, Products, and Powers Of Congruences")

Edit or AddNotationAxiomatic Method

This work was contributed under CC BY-SA 4.0 by:

This work is a derivative of:

(none)

Bibliography (further reading)

[8152] Jones G., Jones M.: “Elementary Number Theory (Undergraduate Series)”, Springer, 1998

[1272] Landau, Edmund: “Vorlesungen ├╝ber Zahlentheorie, Aus der Elementaren Zahlentheorie”, S. Hirzel, Leipzig, 1927