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.

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