Modern mathematics: odd number, also known as odd number, is an important number, that is, an integer that cannot be divisible by 2. Odd numbers are often expressed as 2n+ 1 or 2n- 1, where n is an integer. Even number, also called even number, is an important number, that is, an integer divisible by 2. Even numbers are usually expressed as 2n, where n is an integer. The sum, difference and product of even numbers are even numbers.

Primary school mathematics: Beijing edition textbook, 2004, 10 volume, 5 1 page, puts forward that the number divisible by 2 is called even number; Numbers that are not divisible by 2 are called odd numbers. Page 12 of the fifth grade textbook 20 13 of People's Education Press puts forward that among natural numbers, numbers that are multiples of 2 are called even numbers (0 is also even numbers), and numbers that are not multiples of 2 are called odd numbers.

Two. Conceptual explanation

In natural numbers, it is either odd (also called odd) or even (also called even). Generally speaking, even numbers are represented as 2n; The odd number is 2n+ 1, and n is an integer.

Natural numbers include 0. So 0 naturally becomes an even number. 0 is a special even number.

Primary school stipulates that 0 is the smallest even number and 1 is the smallest odd number. However, what I learned in junior high school is a negative number. When there is a negative even number, 0 is not the smallest even number. Like -2, -4, -6, -8,-10,-12 are all negative even numbers; When there are negative odd numbers, 1 is not the smallest odd number. Things like-1, -3, -5, -7, -9,-1 1 are all negative odd numbers.

Even numbers include positive even numbers, negative even numbers and 0. Odd numbers include positive and negative odd numbers.

In decimal system, you can judge whether the number is odd or even by looking at the single digits: 1, 3, 5.7 and 9 are odd; Numbers with digits 0, 2, 4, 6 and 8 are even numbers.

Some properties about odd and even numbers are as follows:

① One of two consecutive integers must be odd and the other must be even.

(2) The parity of the sum of two integers-odd+odd = even, odd+even = odd, even+even = even. Generally speaking, the sum of odd numbers is odd, the sum of even numbers is even, and the sum of any even numbers is even.

③ Parity of the difference between two integers-odd-odd = even, odd-even = odd, even-even = even, even-odd = odd.

(4) The parity of the product of two integers-odd× odd = odd, odd× even = even, even× even = even. Generally speaking, in integer multiplication, as long as one factor is even, its product must be even; If all the factors are odd, then their products must be odd.

⑤ Parity of quotient of two integers-In the case of divisibility, even divided by odd is even, even divided by even may be odd or even, and odd cannot be divisible by even.

⑥ If both A and B are integers, the parity of a+b and a-b is the same.

Except 2, all positive even numbers are composite numbers.

The sum of two adjacent integers is odd, and the product of two adjacent integers is even.

Pet-name ruby If an integer has odd divisors, then this number must be a complete square number (such as 1, 4,9,16,25, etc. If a number has an even number of divisors, then this number must not be a complete square number.