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even number∗
mathcam†
2013-03-21 16:37:27
Definition Suppose k is an integer. If there exists an integer r such that
k = 2r + 1, then k is an odd number. If there exists an integer r such that
k = 2r, then k is an even number.
The concept of even and odd numbers are most easily understood in the
binary base. Then the above definition simply states that even numbers end
with a 0, and odd numbers end with a 1.
0.0.1
Properties
1. Every integer is either even or odd. This can be proven using induction,
or using the fundamental theorem of arithmetic.
2. An integer k is even (odd) if and only if k 2 is even (odd).
∗ hEvenNumberi created: h2013-03-21i by: hmathcami version: h34703i Privacy setting:
h1i hDefinitioni h11-00i h03-00i
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