Show that if an integer n is not divisible by 3, then n2 – 1 must be a multiple of 3
If is not divisible by 3, then either or
Then
Let We know that is an integer because is an integer. Therefore equals 3 times some integer. So is a multiple of 3.
Or
Let We know that is an integer because is an integer. Therefore equals 3 times some integer. So is a multiple of 3.
Therefore if an integer is not divisible by 3, then must be a multiple of 3.
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