Answer to Question #273405 in Discrete Mathematics for haji

Question #273405

Use a direct proof to show that every odd integer is the difference of two squares.  


1
Expert's answer
2021-12-01T05:05:47-0500

Let aZa\in Z . Let's consider M=(a+1)2a2=a2+2a+1a2=2a+1M=(a+1)^2-a^2=a^2+2a+1-a^2=2a+1 . Formula 2a+12a+1 is the general formula for an odd number, so every odd number can be written as the difference of two squares. Thus, the statement has been proved.


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