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

User Dimi
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1 Answer

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Answer:

Proved

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


a=2m+1\\b=2n+1, for some integers m and n.

Now product

=
ab =(2m+1)(2n+1)\\= 4mn+2m+2n+1\\=2(2mn+m+n)+1

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

Then product
ab =2s+1

again gives remainder 1 when divided by 2

Hence product is odd.

User Rita Azar
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