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Show that the cube of a positive integer...

Show that the cube of a positive integer of the form `6q+r,q` is an integer and r=0,1,2,3,4,5 is also of the form 6m+r

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To show that the cube of a positive integer of the form \( n = 6q + r \) (where \( q \) is an integer and \( r = 0, 1, 2, 3, 4, 5 \)) is also of the form \( 6m + r \) for some integer \( m \), we will follow these steps: ### Step 1: Define the number Let \( n = 6q + r \), where \( q \) is an integer and \( r \) can take values \( 0, 1, 2, 3, 4, 5 \). ### Step 2: Cube the number We need to find \( n^3 \): \[ ...
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