Use a direct proof to show that the product of two odd integers is odd

Proved

Step-by-step explanation:

Let a, b be two odd numbers

We know odd numbers give remainder as 1 when divided by 2

Hence a and b can be written as

, for some integers m and n.

Now product

=

We have when m and n are integers, 2mn+m+n also will be an integer say s

Then product

again gives remainder 1 when divided by 2

Hence product is odd.

you need a common difference between consecutive terms to be constant, like 1,2,3,4 or 2,4,6,8, or 1,3,6,9

in mathematics, a function is a relationship between two variables such that the value of one of the variables, called the dependent variable, is determined by the value of the other variable, called the independent variable. there is a specific term we use to describe the set of independent variables of a function.