An odd number is an integer that is not divisible by 2. The mathematical expression is 2k+ 1. Odds can be divided into positive odd numbers and negative odd numbers.

definition

Among integers, numbers that are not divisible by 2 are called odd numbers [1]. In daily life, people usually call positive odd numbers singular, as opposed to even numbers [2]. Odd numbers can be divided into positive and negative odd numbers. The mathematical expression of odd numbers is:

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

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

nature

Regarding odd and even numbers, there are the following properties:

(1) Two consecutive integers must have an odd number and an even number;

(2) Odd number+odd number = even number; Even+odd = odd; Even number+even number+...+even number = even number;

(3) Odd-odd = even; 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 and 9; Even numbers are 0, 2, 4, 6, 8;

(7) Divide the square of odd numbers by 2, 4 and 8, and the remainder is1;

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

(9) The odd number divided by 2 is 1.