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Show that square of any positive integer...

Show that square of any positive integer is of the form of `5m,5m+1,5m-1` for some integer m.

Text Solution

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`(5n-2)^2=25n^2+4-20n=5(n^2-4n+1)-1=5m-1`
`(5n-1)^2=25n^2+1-10n=5(5n^2-22n)+1=5m+1`
`(5n)^2=25n^2=5(5n^2)=5m`.
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