# One dividing a po

Using Euclid’s division lemma –

n = 9(q) + 7, where q is the quotient when divided by 9.

Using this, we have

3n - 1 = 3(9q + 7) - 1
⇒ 3n - 1 = 27q + 21 - 1
⇒ 3n - 1 = 27q + 20
Now, we have to set the above equation in a way, such that
3n - 1 = 9q' + r', where 0 ≤ r < 9

⇒ 3n - 1 = 27q + 18 + 2
⇒ 3n - 1 = 9(3q + 2) + 2

According to Euclid's divison lemma, we have
r = 2, when 3n - 1 is divided by 9

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