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Proof

(related to Corollary: Sums, Products, and Powers Of Congruences)

• The sum and product formulae follow by induction from the proposition about addition, subtraction and multiplication of congruences¹.

• The power formula follows from the product formula by setting $a:=a_1=\ldots=a_r.$

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References

Bibliography

1. Landau, Edmund: "Vorlesungen über Zahlentheorie, Aus der Elementaren Zahlentheorie", S. Hirzel, Leipzig, 1927

Footnotes