Prove the Product of four consecutive positive integers cannot be a perfect Square

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Let N be the first of four consecutive positive integers.

Then assume that is a perfect square.

Also

Since two squares cannot differ by one, we have shown is NOT a perfect square!

Note that another way of looking at this problem is that we  proved that the product of four consecutive positive integers increased by 1 is a perfect square.

If you liked the logic associated with this mathematical proof, then you would probably also like chess which involves the same type of reasoning and thinking.

 

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