Math CentralQuandaries & Queries


Question from bailey, a student:

Prove that the square of any odd number, decreased by 1, is divisible by 8


Hi Bailey,

An odd integer is one more than an even integer so if $m$ is an odd integer then there is an integer $n$ so that $m = 2n + 1.$ Square $m$ and then subtract 1. You will see that what results has a factor of $4.$ The remaining factor is divisible by $2.$ do you see why?


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