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The addition, subtraction and multiplication of even and odd integers obey simple rules. The addition or subtraction of two even numbers or of two odd numbers always produces an even number, e.g., 4 + 6 = 10 and 3 + 5 = 8. Conversely, the addition or subtraction of an odd and even number is always odd, e.g., 3 + 8 = 11. The multiplication of ...
A singly even number can be divided by 2 only once; it is even but its quotient by 2 is odd. A doubly even number is an integer that is divisible more than once by 2; it is even and its quotient by 2 is also even. The separate consideration of oddly and evenly even numbers is useful in many parts of mathematics, especially in number theory ...
The best known result currently stems from the proof of the weak Goldbach conjecture by Harald Helfgott, [15] which directly implies that every even number n ≥ 4 is the sum of at most 4 primes. [16] [17]
Even and odd numbers have opposite parities, e.g., 22 (even number) and 13 (odd number) have opposite parities. In particular, the parity of zero is even. [2] Any two consecutive integers have opposite parity. A number (i.e., integer) expressed in the decimal numeral system is even or odd according to whether its last digit is even or odd. That ...
The standard definition of "even number" can be used to directly prove that zero is even. A number is called "even" if it is an integer multiple of 2. As an example, the reason that 10 is even is that it equals 5 × 2. In the same way, zero is an integer multiple of 2, namely 0 × 2, so zero is even. [2]
There exists a natural number such that every even integer larger than is a sum of a prime less than or equal to and a number with at most two prime factors. In 2025, Daniel R. Johnston, Matteo Bordignon, and Valeriia Starichkova provided an explicit version of Chen's theorem: [ 7 ]
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Characterise word-representable near-triangulations containing the complete graph K 4 (such a characterisation is known for K 4-free planar graphs [128]) Classify graphs with representation number 3, that is, graphs that can be represented using 3 copies of each letter, but cannot be represented using 2 copies of each letter [129]