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## 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]

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