What are the concepts of odd and even numbers?

Odd number (English: odd number), also known as odd number, is even, and the odd number is 1, 3, 5, 7, 9. Even numbers can be represented by 2k, and odd numbers can be represented by 2k+ 1, where k is an integer.

All integers are either odd or even. If a number is a multiple of 2, it is even (even), which can be expressed as 2n; Otherwise, it is odd (singular), which can be expressed as 2n+ 1(n is an integer), that is, the remainder of odd (singular) divided by two is 1.

Extended data:

I. Odd number classification

Odd numbers can be divided into positive and negative odd numbers. The mathematical expression of odd numbers is 2K+ 1(K≠0).

Positive odd numbers: 1, 3, 5, 7, 9,1,13, 15, 17, 19, 2/kloc-.

Positive odd numbers:-1, -3, -5, -7, -9,-1,-13,-15,-17,-/kloc.

Second, the nature of odd and even numbers

1, there must be an odd number and an even number in two consecutive integers.

2, odd number+odd number = even number; Even+odd = odd; Even+even+...+even = even.

3. Odd number-odd number = even number; Parity = odd number; Odd-even = odd.

4. If A and B are integers, the parity of a+b and a-b is the same, that is, a+b and a-b are both odd or even.

5. The product of n odd numbers is odd, and the product of n even numbers is even; If one of the formulas is even, the product is even.

6. Odd numbers are 1, 3, 5, 7, 9; Even numbers are 0, 2, 4, 6 and 8.

7. If the square of an odd number is divided by 2,4,8, the remainder is 1.

8. The square difference between any two odd numbers is a multiple of 2, 4 and 8.

9. The remainder of an odd number divided by 2 is 1.

Baidu encyclopedia-odd number

Baidu encyclopedia-even number