Proof by Contradiction: Odd and Its Square

We have had several examples on proof by contradiction in this blog like irrationality of square root of 3 and the sum of root of 2 and root of 3. In this post, we will have another detailed example. In proof by contradiction, we want to change the statement “if P then Q” to “if NOT Q then […]
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Square of Odd Numbers Minus 1

Many numbers have interesting properties worth investigating. These properties can be used to introduce the notion of proofs. Teachers may try this out in middle school or high school students. Although the proofs might not be as elegant or as formal such as written in books, its notion and the reasoning behind it is more […]
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Proof of Divisibility by 8

If you have read the discussion on divisibility by 4, the proof for divisibility by 8 is somewhat similar. To know that the number is divisible by 4, we just have to look at the last two digits. In divisibility by 8, we look at the last three digits. For example, the number 10938648 is divisible by […]
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