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Definition: Even and Odd Numbers

An integer $n$ is called even, if it is divisible by $2$ (i.e. $2\mid n$), otherwise (i.e. if $2\not\mid n$) it is called odd.

Examples

• $0,2,10,-20,250,\ldots$ are even.
• $1,-1,3,-3,255,-33,\ldots$ are odd.

Table of Contents

1. Proposition: Every Integer Is Either Even or Odd
2. Proposition: Product of Two Even Numbers
3. Proposition: Product of Two Odd Numbers
4. Proposition: Product of an Even and an Odd Number

Mentioned in:

Algorithms: 1
Corollaries: 2 3 4
Definitions: 5 6 7 8 9
Examples: 10 11
Explanations: 12
Lemmas: 13 14 15
Problems: 16
Proofs: 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41
Propositions: 42 43 44 45 46 47
Sections: 48 49
Theorems: 50 51 52 53 54 55 56 57

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References

Bibliography

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