In mathematics, a singly even number is an integer divisible by 2 but not by 4, i.e., an integer of the form 4n + 2. Such a number can be divided by 2 only once, hence the name; it is even but its quotient by 2 is odd. A doubly even number is an integer that is divisible by 4, i.e., an integer of the form 4n. In this terminology, a doubly even number may or may not be divisible by 8, so there is no pattern extending to "triply even" numbers. The separate consideration of singly and doubly even numbers is useful, for example, in the theory of even codes.
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Properties
A singly even number cannot be a powerful number. It cannot be represented as a difference of two squares. However, a singly even number can be represented as the difference of two pronic numbers or of two powerful numbers.
History
The ancient Greeks formulated similar concepts, generally translated as even-times-even and even-times-odd numbers. These terms were given various inequivalent definitions by Euclid and later writers such as Nicomachus.[1]
References
- ^ Euclid; Johan Ludvig Heiberg (1908). The Thirteen Books of Euclid's Elements. The University Press, pp. 281-284.
External links
- A016825 Numbers congruent to 2 mod 4 at the OEIS
- A008586 Multiples of 4 at the OEIS
