Given that 2m - 1 = (2n + 3)^2, where n is a positive integer. Show that m is an integer.

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Worked solution

1. Expand the squared expression and equate it to $2m-1$.

$2m-1=(2n+3)^2$

$2m-1=4n^2+12n+9$

2. Rearrange to obtain $m$ and justify that it is an integer.

$2m=4n^2+12n+10$

$m=2n^2+6n+5$

Since $n$ is a positive integer, $2n^2$ , $6n$ and $5$ are integers. Hence $m$ is an integer.

Answer

Since $m=2n^2+6n+5$ and $n$ is an integer, $m$ is an integer.

AI analysis — may contain mistakes.

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