doubly even number
A doubly even number is an even number divisible by 4 and sometimes greater powers of two. If is a doubly even number, it satisfies the congruence . The first few positive doubly even numbers are 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, listed in A008586 of Sloane’s OEIS.
In the binary representation of a positive doubly even number, the two least significant bits are always both 0. Thus it takes at least a 2-bit right shift to change the parity of a doubly even number to odd. These properties obviously also hold true when representing negative numbers in binary by prefixing the absolute value with a minus sign. As it turns out, all this also holds true in two’s complement. Independently of binary representation, we can say that the -adic valuation (http://planetmath.org/PAdicValuation) of a doubly even number with is always or less.
All doubly even numbers are composite. In representing a doubly even number as
If is doubly even, then the value of (the divisor function) is even except when all the nonzero in the factorization are greater than 1.
Whereas whether is singly or doubly even, with the imaginary unit it is the case that only when is doubly even.
|Title||doubly even number|
|Date of creation||2013-03-22 18:09:38|
|Last modified on||2013-03-22 18:09:38|
|Last modified by||1and2and4 (20899)|