Use Euclid's division lemma to show that the cube of any positive integer is of the form `9m`, `9m+1`or `9m+8`.
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To show that the cube of any positive integer is of the form \(9m\), \(9m + 1\), or \(9m + 8\) using Euclid's division lemma, we will follow these steps:
### Step 1: Understand Euclid's Division Lemma
According to Euclid's division lemma, for any integer \(A\) and a positive integer \(B\), there exist unique integers \(q\) (the quotient) and \(r\) (the remainder) such that:
\[
A = Bq + r
\]
where \(0 \leq r < B\).
...
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